The Maverick I know of wasn't born in '03 so no, not the same one.
I haven't seen either topgun movie and have no desire to, so that character (or John McCain) isn't what I think of when I hear "maverick." I think of the trait. And naming a child based on trait (e.g. Charity, Patience, Prudence etc.) is much less common now so that makes it a little odd to me. Plus, I don't view "maverick" as a good thing. Because it means "independent" but I also associate it with being reckless, not thinking things through, and being too independent.
So to my ear, naming your child "Maverick" is like naming your child "Rude" or "Impatient."