Tamsin is an easy choice. It has never been popular in the USA but is easy to spell and pronounce. It is only two syllables, so it doesn't need a nickname.
Tamsin has an old-fashioned feel and also reminds me of the fictional works of
Peter S. Beagle.
Tallulah is a bit ridiculous. It sounds like something a celebrity would use.
Tracy is dated, one-time hit, and reminds me of
Spencer Tracy, the old flame of
Katherine Hepburn. If I had to use a flash-in-the-pan name from around that time, I would prefer
Trudy.