It sounds to me like your ex-husband's priorities are misplaced. He should be considering his children's feelings first. Grown-ups are expected to have the maturity to deal with difficult topics and situations. This is unfair to expect from children (and I would argue that it is emotionally and psychologically abusive for them to be asked such a thing).

If his girlfriend is uncomfortable with topics that involve some of the most important people in his children's lives, then that is her issue to deal with, not theirs. It's probably not your place, but it sounds like someone should suggest to your husband's girlfriend that she seek therapy to work on whatever is making her uncomfortable whenever yours or your family's names are brought up.