fuzzy about genders but only half way.
bel ami = male,
belle amie = female.
bellamie or bellamy = grammatically wrong
same for the other one, for female it should be "bonne amie".
Just as additional info :)
Seeing that
Amy though is a form of "Aimée", maybe Bellamy is supposed to mean "
Belle Aimée" = "beautiful Beloved" or "beautiful and beloved".