I believed for years that my good friend’s dad’s name was Aba and even called him that once before I realized later that it’s the Hebrew word for father.
I had been having complex thoughts for years at that point so it was a bit embarrassing.
Technically 'daddy' is a name.
A name is fundamentally just a label that we use to identify other people and objects. Post Malone, your first and last name are part of the universal naming system like the Kilometer, and 'daddy' is a personal system relative to the conscious experience of the user.
"daddy" is a kinship term, or familial title. It's a noun, and a mode of address, but it isn't a name, technically or otherwise. There are a few posts in this very thread about children realizing that "daddy" isn't just their father, but anyone's.
Much like when you refer to a doctor as "doc", or a professor as "professor".
To prove the point, there are people who have more than one person in their lives whom they call "Dad" or whatever variation. Raised by a gay couple, or close enough to a stepfather to think of him in those terms. Most of us only have one "Dad", but this isn't universal, and we all know that everyone has one, whether they refer to him that way, or even know him at all.
I had been having complex thoughts for years at that point so it was a bit embarrassing.