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?

Finally a proper use of this meme

Why do shapeshifters need a family?

They could do a mitosis.

It's Oedipus with a single parent playing both roles.

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.

Its just smells

Moonbeam?

This is why I like the idea of monster languages. All the changelings can speak changeling, which while it isn't used for full conversations, they might go "y'know, the... er-uh, boss?" and it's slipping in a codeword like "trust?"

They got that Fey smell

Moonbeam.

D&D doesn't have incest rules, so it doesn't matter.