Higuchi san is right. I am just adding Hansamu here to indicate the English way to write it.

Hansamu is nothing more than a Japanese rendition of the English Handsome. The meaning is identical and hansamu is indeed used as a loan-word in Japanese.

Have fun. Maybe it'll give you a reason to learn this unique language and learn more about this fantastic culture.

Just an alternative suggestion for your puppy's name, although it doesn't mean 'handsome' at all:

I recently had an acquaintance (who didn't know I was a Japanese-speaker) tell me about the naming of her pet, a cat named "Suki."
She pronounced the name "Soo-key" (the correct pronunciation is really more like s'ki or 'ski') and she told me confidently it was Japanese for 'love' (it's really Japanese for 'like,' although it's true that people may say "suki" to each other to say 'I love you' in a conservative-kinda way....)

Well, although not technically 100% correct, I did think the name had a charming sound to it when pronounced as "Soo-key"...
Anyway, that was a cat, your pet is a puppy, so you may not think it appropriate, but it did strike me as cute at the time.

Good luck with your beautiful pup. :-)