It sounds nice with the Hebrew pronunciation, but Chava would cause bullying in England because it looks like that nasty word "chav" used to describe lower-class people.
I like this a lot. It doesn't have the Christian connotations of "Eve," "Ava" or any of those variants, and it doesn't look like it would be pronounced "Have-a" like "Hava." I imagine it with a gutteral "H" sound like Channah or Chaim, but I like the hard "K" sound better.