No, it feels forced to me.
Gaia is a separate name with a different etymology and stands nicely on its own.
I'd just call her
Gaia if I wanted to call her that.
If you want
Gabriella on the birth certificate but no
Gabby I would try
Ella, it makes more sense as it is included in the name. But I would still just use
Ella.
To be honest I don't really understand why you want to use it if you don't want to call her that? Name her
Gabriella and call her
Gabriella. It has four syllables, it can work without a nickname. I know several people who go by their full names even though they have three or four syllables.
She might become
Gabby at school and I guess you couldn't do anything about it. Maybe you want to prevent that by offering
Gaia? I don't think it will stick, sorry! It might if you called her
Gaia since birth and she'd introduce herself as
Gaia, not
Gabriella, but then you might as well name her
Gaia. People will probably be a bit confused and think there was a mistake if she is suddenly listed as
Gabriella as the connection isn't obvious.
So I think it will cause trouble and not really work. Sorry!
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