I've got to say I didn't think Alicia was necessarily a modern name at all. So I looked it up, and it's the Latinized form of Alice, which is a Germanic name, via Old French, via Old High German, none of which are terribly modern languages.

Tiffany was a name popularly given in Old French and Middle English -- languages spoken in the early Middle Ages -- to girls born on Epiphany Day (Tiffany being related to the Latin Theophany, another word for "epiphany").

So even if the names were chosen at random, they're not anachronistic :)