The name is not, and never has been, unique to Hispanics or Indians. I can understand being a bit leery of naming a child something that screams a completely different ethnicity, but I find this question ridiculous.
In all honesty, I don't see what the dilemma is at all for you. You call the baby
Gabriella. Everyone else calls the baby
Gabriella. You like the name
Gabriella. Why don't you just use it and be done with it?
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"What are these parents thinking?...Let's name her Madison--she'll live in her own world: 16 square miles surrounded by reality." -- Susan Lampert Smith