Short answer - no!
There's no reason why any HR department would waste its time doing this officially and please don't imagine that big business is all interlinked in a spooky, matrix sort of way.
Furthermore, it is sailing very close to the wind in terms of employment law and data protection, it is quite probably in breach of the Human Rights Act 1998 and may well constitute a civil wrong against the person who is subject to this.
Therefore, in interviews, if you think it helps you demonstrate you interest and commitment to a field of work, then mention who else you have applied for. If a firm likes you it will work in you favour to think that they are competing to employ you.
However, should you see a funny looking man in a suit suddenly appear out of nowhere and call you 'Mr Anderson' I'd run like hell!!