Interestingly enough, her (apparent) birth surname of Navarro is Basque-derived, not even Spanish, just to mix things up some more. https://en.wikipedia.org/wiki/Navarro_(surname)
I have my own theories about Gina's name (including that it is Regina) but it should be noted that "Regina" in Spanish is not pronounced the way that would lead to "Gina". https://www.behindthename.com/name/regina
However, I can also see Elena liking the name and nickname and not caring. Cross-cultural names are a thing, and Gina is not as far out as naming her "Harriet", or something.