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?
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.
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.
Pathfinder changelings are very different from D&D changelings which is what the meme is referencing. D&D changelings are a race of shapeshifters from the Eberron setting. Pathfinder changelings are the children of hags and are overall closer to the actual folklore of a changeling.
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?"