It is apparently not just pride or vanity that is behind this. According to Clive Chajet, chairman and chief executive of the 'identity and image management' consultants Lippincott & Margulies, 'there's a feeling' within the company that if Gillette was better understood for what it is - a manufacturer and marketer of a broad range of products - it would become more valued by the investment community.
Separate from, but related to, this is Gillette's desire to transfer to all its products the impression of superior technology associated with its razors and blades. It wants the public to buy all its products at least partly because they have the Gillette ring of quality.
Lippincott & Margulies, which seems proud to be accused of inventing the term 'corporate identity', has responded to this ambition by devising 'some identity tools' that are only to be used at the corporate level rather than for promoting the brands. 'They hopefully over time will create for Gillette an image separate from shaving products. Not better, nor worse, but separate,' Mr Chajet said.
It is not altogether surprising to find among these tools a new logo. But Mr Chajet claims a fresh departure in the 'corporate positioning phrase'. This is what Gillette representatives are supposed to say whenever they are thinking corporately and it runs as follows: 'The Gillette companies - world-class brands, products and people.'
It sounds innocuous - and meaningless - enough. But Mr Chajet insists that the wording has been carefully chosen. 'We used the phrase 'world-class' because Gillette is not perceived as an international company. Although it was one of the first international brands, it is regarded as a US company.'
And this is the rub. Mr Chajet sees the internationalisation of business as an unstoppable trend. 'We've found increasingly that corporations are in communications leaving their passports at home,' he said.
For example, 10 years ago the Britishness of Jaguar was seen as fundamental to the car's brand image. Now it is part of Ford and therefore American. Some might believe that the marque has suffered as a result, but Mr Chajet believes that the place of origin has become largely irrelevant.
In the same way, Chrysler, one of the big three US car makers, launched its new Neon model in Germany. Meanwhile, the decision of one of Korea's biggest companies, Samsung, to use Roman letters in a new promotional campaign is evidence of a desire to break out of the Asian market.
All these moves are signs of a growing trend for corporations to try to adopt 'as global an image as possible', Mr Chajet said, although he acknowledges that the transformation from regional to global entity is not yet complete - witness the enduring relationship between Switzerland and watches and the fact that Mercedes-Benz still seems to see its country of origin as vital to its success.
A recent study by AC Nielsen, the market research company, suggests that - for all the cross-border marketing activity - the popularity of certain brands differs from country to country and from region to region. As a result, Coca-Cola - a client of Mr Chajet's firm - is the overall brand leader in three countries, but Ariel and Persil detergents are just behind it in Britain, Danone yoghurt takes second place in Spain and Langnese ice cream the same spot in Germany.
Companies must respond to 'different national habits', Mr Chajet said. But the best way to do it is through advertising and PR efforts aimed at individual markets. 'The broad strategic attack should be an overall campaign.'
And he has a warning to those who remain stuck on the importance of nationality. He reckons that just as the value of multi-million-dollar star endorsements can be threatened when the star either retires, as Nike's main man Michael Jordan just has, or runs into a bad press like Michael Jackson, the pop star who has a lucrative contract with Pepsi, so too can businesses suffer from association with countries.
What would happen to the popularity of French wines if France suddenly invaded Poland? 'If you link your image to an aspect over which you have no control you risk danger,' he said.
Consequently, his firm is a strong proponent of building a company's image around its 'proprietary assets' - things that are unique or at least owned or controlled by the company itself. They might include names, logos or - in this technological age - design systems.
But while opinion on the value of brands is sharply divided, these assets are only of any worth as long as the company has a good reputation. So the successful managers must have as much awareness of what can hurt an image as what can build it. When making decisions they must take into account environmental concerns and other social issues as well as financial factors.
As Mr Chajet points out, business is becoming a news story, with much more space in all forms of media devoted to it than ever before. Years ago, senior executives used to breathe a sigh of relief every morning when their companies failed to merit a mention in the morning papers. Now the chances of that happening are much reduced. 'Therefore top management has to pay attention to this subject,' Mr Chajet said, adding that it can have a far greater bearing on corporate performance than is often recognised.