This coat hanger is low profile, very strong, nice looking, and only cost about $0.34 in filament to print.

The lower hook is designed for hanging keys or a lanyard; and is tucked back so a coat can be easily hung on (and removed from) the larger hook without knocking the keys off. Likewise, it can be used for a lighter jacket.

I haven't tried it, but I'm confident that this hook would be perfectly suited for a purse, as long as the strap is narrow.

Also available on Makerworld: https://makerworld.com/en/models/631827#profileId-556796

Enjoy!
-Steve