The recommendation is contained in a confidential report for the ITV companies prepared by the management consultants Bain & Co, which argues that it would help unify the network in the face of increasingly tough competition from the BBC, Sky and Channel 4.
Some ITV companies worry, however, that the network's regional identity could be lost if output is branded under a single Channel 3 umbrella.
Mr Eyre, currently chief executive of Capital Radio, takes up the newly created ITV post in the autumn with a remit to unify ITV. One way of doing this would be to substitute regional logos on peak-time programming with a single Channel 3 logo, according to Bain & Co
Such a move, its supporters argue, seems increasingly logical as ownership of the majority of the 15 franchises now rests in the hands of three big players - Carlton Communications, Granada Group and United News & Media.
The Bain report recommends that, between 7pm and 11pm, programming should appear under the banner of Channel 3, rather than bearing the logo of each regional franchise.
The suggestion - one of a range of ideas from Bain about the future of ITV - has met with strong resistance in the television industry, even if it has found some sympathy among advertisers and media buyers.
Scottish Media Group in particular feels a single Channel 3 brand would detract from the company's regional identity. A source at Scottish said: "We believe very strongly in the identity of Scottish Television. People here don't talk about ITV: they talk about Scottish."
A senior source from another ITV company added: "One of ITV's strengths is its regionality. You wouldn't want to ditch that."
Chris Smith, Secretary of State for National Heritage, warned earlier this month that the regional characteristics of the ITV franchises should not be lost in the rush to consolidate.
However, some within the industry are in favour of doing away with regional identities so that ITV could then be sold to advertisers as a national brand.
Martin Bowley, managing director of Carlton UK Sales, said: "We're competing against uniform networks like the BBC. What does a viewer care if the programme's from Carlton or Granada? It's the quality that matters."
ITV has already moved towards creating a coherent brand with the "Britain's most popular button" advertising campaign. However, the ad has not been a success, and one of Mr Eyre's tasks, as he replaces the Network Centre and ITV Association structure with the new "ITV Ltd", is to decide on a new marketing strategy to help prevent further loss of viewers.
ITV's share of viewing has slipped from more than 36 per cent at the beginning of the decade, to around 32 per cent in the latest estimates.