I like
Carissa. It is pretty and it doesn't seem as princessy and snooty as the similar
Marissa and
Larissa. It is uncommon but doesn't seem unusual and is easily recognisable as well which is great in a name IMO.
I prefer
Caris- I generally like simpler names.
Caris is short and sweet and I love the meaning. I prefer
Carissa to
Karissa. The C looks prettier to me and the K makes the name look a little trendy.
Carissa looks more classic to me. I think I like
Caris and Karis pretty much the same though. I would prefer
Charis or
Carys to both though.
I don't think either
Carissa or
Caris are too close to
Christine /
Chris. Definitely not too strange for a mother and daughter