I like Gene (actually I love it - it was our list but got a girl!), and Eugene is fine. Better than the myriad Charlie / Harry / Ben type names out there.
I don't really get the need to have a fashionable name at all. Fashions come and go, and choosing something 'cool' and 'on trend' today will probably result in them sounding very Wayne and Sharon-like in 20-30 years.
Pick a name you love. Who cares if it reminds someone of their friend's auntie's dog's best mate? Gene has so many positive namesakes:
Gene Roddenbery
Gene Wilder
Gene Hackman
Yep. Love it.