Parental terms for same sex mothers or transgender parent

My significant other is transgender. This is a recent coming out. We currently are trying to have a baby so we are talking about what the baby will call her once they can talk. Obviously daddy doesn't feel right anymore. We currently use parental terms when talking about the dog. We have time to figure out what will work for the baby but would like to try some out with the dog.

What do some of you parents already use. I have a couple of friends are both mom or 1 is mama the other is mommy. I have heard suggestions of using a different term altogether. My so isn't sure if she'll want to be a variation of mom because she doesn't feel very maternal and sees that as my title. Do any of you have a ambiguous parental title or a suggestion we could start trying?

Thanks :)