I wouldn't ignore your child when she says 'Trevor'. Instead I would model using 'daddy' instead. E.g.
she says 'Trevor, want juice'.
You react more slowly and say 'Daddy is getting you juice'.
In contrast when she calls you 'Daddy' respond faster and reinforce her for it. E.g.
DD: 'daddy, want juice'
You immediately turn and smile and ticlkle, kiss etc when saying! "Of course, daddy will get you some juice, you asked so nicely'
Not sure why you are adding 'father' into the mix for a two-year old. It just sounds weirdly formal and might confuse her further.
You can also play games with her and model what you want her to say e.g. on the swings ask her to 'say "Daddy push me"!'
Also do lots of narration while you are doing things together. E.g.
Daddy is getting the eggs, oops daddy nearly dropped one, daddy is cracking the eggs in a bowl, do you want to help daddy? Ok say 'daddy lift me up!'. Etc.
If your OH has been referring to you as Trevor to your child that is highly odd. E.g. 'Trevor is putting you to bed'. You need to get her on board and let her know how uncomfortable and anxious is is making you feel.
I'm glad it seems to be improving but stressing less about it would also probably help your relationship. The amount of times you have felt you have had to say you love your daughter is telling.