The current Tate of the nation

So farewell then, Tate Gallery. And welcome, Tate Britain. But does the new name and the radical rearrangement now make more sense of its collection? And what will be the effect on its growing family of galleries?

One of the small but continual humiliations of late capitalism is the coercive-collusive brand name. Weekend Super-Saver, BT Together, Chicken McNuggets - if you want certain goods and services, you have to say certain words. But these words don't just designate. They celebrate. You can't mention one of these products, without - however unwillingly - joining in, without gratefully applauding the excellent product and its benevolent provider. I feel the same way about Tate Britain. This is the name of the new Tate Gallery of British art, which opened last week in the building on Millbank that was formerly the Tate Gallery simple. But what a name! Tate Britain: just to say it is to speak a corporate logo, to wave a flag for the vast, dynamic, efficient art organisation which is Tate (comprising Tate Britain, Tate Liverpool, Tate St Ives and - from May - Tate Modern). The name itself puffs. But it's the name we'll have to use.

Apart from that, I feel fairly positive about Tate Britain. It makes sense to separate out the Tate's twofold collection into its parts, British art post-1500 and international art post-1900. The latter goes to Tate Modern on Bankside. Post-1900 British art may turn up at either venue. It also makes sense to show British art in isolation; it is sufficiently insular. And the new all-British rehang turns these familiar galleries - some still closed for renovation - into a maze of surprises.

But I suppose one should emit a small sigh too. Strange to think you'll never again see that suite of gloomy late Rothkos in this building, never again see Picasso's Three Dancers here either, nor Matisse's giant papier- colle Snail, or a Bonnard, or a Dali, or Boccioni's striding futurist bronze figure. In fact the only definite foreigner to escape the winnowing is Andre Derain, with his fauvist picture of The Port of London. Subject matter ruled there.

It rules the rehang as a whole. It doesn't go chronologically, from old Tudors to young Turks. It goes thematically. Each room takes a subject heading - the land, the city, fantasy, abroad, portraits, nudes etc - to gather a miscellany, juxtaposing works from all periods. Wyndham Lewis hangs by Joshua Reynolds, Etty by Uglow, Fuseli by Cecil Collins, Stubbs by Moore, Walter Sickert by Lisa Milroy, that sort of thing. There are also rooms given to individual artists: Gainsborough, Blake, Constable, Ben Nicholson, David Hockney. But not the second DH, and in fact the Young British Artists of the last decade don't appear as prominently as you might expect.

Now none could call this approach intellectually adventurous. And a friend of mine in the Tate, talking about the hang in advance, said it was expected that the public would like it, but the critics wouldn't. Leaving aside the hurtful implication that what we critics say makes no difference to anyone, I expected to agree. But actually it's OK. The layout makes for a decently straightforward showing of wares. No work is being buttressed by an interesting curatorial agenda. Each stands up for itself.

Or not. If you thought that the Tate had been wholly in thrall to the avant-garde lately, think again. It's been quietly buying some extremely square, not to say rum, contemporary oil paintings and I'm afraid - without naming any names - that there are corners of this opening show that could well have come from an RA Summer Exhibition.

On the other hand, some interesting things have come up from the vaults. At least, there's a Thomas Jones "snapshot" painting of Naples that I don't remember seeing before, and a "mad period" Richard Dadd of an imagined middle-Eastern market which is indeed pretty mad.

One room has things practically never seen in the Tate. It's focused on Hogarth's painting The Roast Beef of Old England, and otherwise contains Hogarth prints and cartoons by Gillray and others, including Steve Bell. But check the labels: apart from the painting, almost all these items are loaned from the British Museum.

The British line of cartoon and caricature - Gillray, Rowlandson, Cruikshank, Ape, Beerbohm, Bateman, Low, Scarfe, Bell - is a big gap in the Tate's collection of British art. It's a serious gap, since this is one of British art's strongest hands. Another gap is vernacular - or naive - art, the art of prize boxers and porkers, in Britain never clearly separate from the fine variety. But these things can of course be borrowed, and hopefully will be. I believe there'll be a Gillray exhibition in the nearish future.

The main special event for this launch is in the central Duveen galleries: three new large sculptures/installations by Mona Hatoum, with the title The Entire World as a Foreign Land. A risky commission. Hatoum's work can be scarifying, in its very direct address to the viewer's body. But sometimes it falls completely flat. You see the effect intended, and you feel it not happening, and I'm afraid it doesn't happen here at all.

Mouli-Julienne (x21) is an enormously magnified manual kitchen vegetable shredder. It dominates the chamber. Perhaps it looks a little like a giant scorpion. It certainly looks like a bit of Sixties heavy-metal sculpture. But what it must be meant to do, and what it doesn't do for one moment, is menace. It's just too cleanly made. Bad concept anyway. And the "dangerous" tableau of household metalware at the other end of the gallery, apparently all wired up to live electricity, with burning-buzz high-voltage sound effects to assist that impression, just provokes a blunt common-sense retort: if you attach a positive and a negative current to, say, the same colander, you don't electrify it, you blow the fuse. Oh well.

Meanwhile, at Tate Liverpool, A New Thing Breathing is a show of recent work by the sculptor Tony Cragg. It was about 20 years ago that Cragg first arrived with his New Stones - a floor scattered with coloured plastic objects and plastic scraps, picked up off the street, but transfigured by the simple ruse of arranging them into a perfect red-violet spectrum. Since then he's left that light-footed scavenger aesthetic far behind. His production values become ever higher and heavier. The creations here - of marble, plastic, stone, glass - are very made and often very large.

They are the devil to describe. And in a way that's the point of them. Cragg takes the modern object world and performs estranging but satisfying variations on it. The elements are basically familiar. Cragg's shapes, materials, textures can be sourced to things we know and use everyday. But their combinations, scale-shifts and transformations put everything in play.

For instance, there is a set of polished stone pieces which clearly takes off from piles of unevenly stacked plates, slipped even further out of kilter, beyond what could possibly stay balanced, and given some wild turns as if the form had gone out of control on a potter's wheel. The stacks become towers of spinning, sliding energy.

Or take another series, in dark bronze. The pieces are horizontal, and the founding motif is a bottle or a vase with a neck. You see this shape at the end of each piece, but then it's extruded sideways, stretched out so that its neck-opening becomes a long mouth, and twisted round and about and opened out, so that what began as a bottle turns into - say - a fantastic double-shelled crustacean or an immensely complicated bit of gadgetry.

This is current Cragg at his most curious and delightful. Elsewhere, regrettably, the play goes dull, particular in the forms covered all over with dice, or perforated all over with large round holes. And all too often the good old modern British semi-abstract lump rears its head and the looming shadow of late Moore and late Caro seems about to claim another victim. And anyway, what's it all about, actually?

People have a go at that one. It's something to do with the natural and the man-made, and with science and technology, and with matter and construction and chaos. Something to do with, yes. But really, all interpretations of Cragg's work are a kind of free association, and so are the pieces themselves. The sculptures are not in the meaning business. They're in the "something to do with" business. They associate from object to shape to material to function to texture and so on in any direction that they please.

Which is fine, I suppose. But it makes the work into an extremely resourceful sort of doodling, and it puts a premium on turning up a real surprise - on introducing some utterly new kind of thing into the world. Cragg has done so sometimes. I think of an extraordinary thing he made about 10 years ago - a stack of I-beams on which were shelved cast-bronze sugar- beets, slashed with halloween faces and oxidised green. Never seen anything like it - and there's certainly nothing like it in Liverpool.

Opening shows: Tate Britain, Millbank, London SW1. Mona Hatoum to 9 July. Every day, free. Tony Cragg: Tate Liverpool, Albert Dock, Liverpool L3. To 4 June, closed Mondays. Entry pounds 3, concs pounds 2