Paul, wouldn't Bells' Architecture be more appropriate? The question referred to OUR family name, and OUR business, so presumably there's more than one Bell: The Bells. In which case Bells' Architecture makes more sense than Bell's Architecture.
I'd go with your other suggestion of Bell Architecture.
Trevor, I agree up to a point. There's no need for a sign or company name to reflect legal ownership, so either Bell's or Bells' would do. And then, of course, many companies drop (or never use) their apostrophe anyway - Lloyds Bank (but not Lloyd's Register), Boots, Barclays.
So pretty much all combinations are defendable:
Bell's Architecture - possessive, of Bell. Bells' Architecture - possessive, of Bells. Bell Architecture - adjectival, architecture of type Bell. Bells Architecture - adjectival, architecture of type Bells.
So just pick one you like! I happen to like Bell's Architecture, especially if one of the Bells is more or less in charge. It'll probably cause the least comment. So I was re-assuring Finnsheart that it is fine, even though she thinks it looks horrible. But I agree with you, Bells' Architecture is fine too. I don't know how you'd decide which is more appropriate - so go with any of them, Finnsheart, and don't worry about it too much!