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?
You would know because you communicate with other changelings through the bond. They know everything about each other.
Finally a proper use of this meme
Moonbeam.
Why do shapeshifters need a family?
They could do a mitosis.
Can they recognize their mitosis sister?
If not, the worst case scenario would be an entire city taken over, Invasion of the Body Snatchers style, but every shape shifter thinks the rest of the city is normal people.
It’s Oedipus with a single parent playing both roles.
D&D doesn’t have incest rules, so it doesn’t matter.
According to Pathfinder lore for changelings, it is unlikely that your dad would have also been a changeling (but I guess it could work).
Also, it would be just a difficult to tell as any other being that gained a transformation spell/ability. Being a changeling doesn’t necessarily give any kind of transformation ability.
Moonbeam?