I think it's up to you of course and if you dislike the name or feel strongly against it because of the connection to his ex, then that's totally legitimate.
However, have you asked your partner why he likes the name kate and wants to consider it? He might just like the name. Plus not every relationship ends badly, so the similarity might not seem a big deal to him and it could be as simple as him considering names he is familiar with, and thinking that's pretty.
There are certainly names of ex's/people in our life we would not choose for our children in a million years. But I wouldn't necessarily disqualify a name/others similar to it on the ex criteria alone.