1. Don’t change the name. The doctor is the doctor, keep it that way. That means no making the name more feminine.
2. Romance isn’t necessary. The doctor’s still married to River, don’t put them into any more relationships. Romance isn’t the centre of the universe and it isn’t the key factor of this show.
3. Don’t put them in a dress or skirt. The doctor does too much running to not be in pants. Also pants are always more comfortable and protective.
4. Don’t make her feminine. Over 2000 years of being a man would probably reflect a lot about your behaviour. Make her a tomboy.
5. Keep her hair short. Long hair gets in the way, and when trying to defend the universe you don’t want to be dealing with hair issues.
6. There is nothing wrong with a male companion. There’s always been a male doctor and a female companion. Switch it up, make the next companion a guy. Have it play out the way it always has, the companion follows the doctor. That’s just how it works.