A changeling might use a different name for each mask and persona and adopt new names as easily as they change faces. The true name of a changeling tends to be simple and monosyllabic; however, there are often accents to a changeling's name that are expressed through shapeshifting, something single-skins will likely miss. So, two changelings might have the name Jin, but one is Jin-with-vivid-blue-eyes and one is Jin-with-golden-nails.
I'm more concerned about why your changeling father is trying to conceal the fact that he is your father from you. It's not like changelings pick a shape and then stick to it forever. He could literally just flick his blue eyes or golden nails or whatever and you would know that it's your dad.
Edit: Wait is this a meta meme about some dude banging his dad?
