Gillian in the UK is very much a name of a specific period - almost all those I know are somewhere between 45 and 58. I don't know anyone in my general circle/age group who uses "an" for hotel, historian or herb. The latter has a particularly strong "h" in most of the UK, so it's not surprising. Yet it comes, of course, from the French "herbe", where the "h" is never pronounced. US practice may well be fossilised, like the use of "gotten" as a past participle.

I'm Gillian too, though only my mother uses my full name.