Well, as long as you don't have a daughter named
Eliza Elisabeth, I think it is fine. I also would steer clear of a daughter
Eliza and a daughter
Elizabeth. If you had say, a
Mary Elizabeth and a
Eliza Jane, it could work out quite well (ie one as a middle name and the other as a first, or even both as middle names would work well).
I think
Eliza is a great name. It has great connection with literature and popular culture, such as with
Eliza Doolittle of My Fair Lady and
Eliza Bennett of Pride and Prejudice.