Since I've never met anyone named
Rhett, nor heard about a single person with this name, so I think, yes, the GWTW association is strong enough. But I don't think that it would be a problem at all:
1.
Rhett is a cool character (JMO)
2. it's not an overused boring
Andrew or
Michael
If you really like the name, I say use it! It sounds nice, it's nice written out, and I prefer it to
Brent :-)