I suppose, but I didn't bother to count her since technically the name skipped a generation and I really don't know how "the Second"s work.

If you want to be technical, I guess Trix would have been Lorelai the First, and so forth.

I actually knew of a man named Kimberly, and his daughter was also named Kimberly. The daughter's now 25, married (with a different last name) with two kids...we still call her "Kim Jr."