What is the full form of desu?

"Desu" is a Japanese grammatical particle, and as such, it doesn't have a "full form" in the sense of an acronym or abbreviation.

However, it does come from the verb "de aru" (である), which means "to be". Over time, "de aru" contracted to "desu".

So, in a way, you could say the "full form" of "desu" is "de aru".

But it's important to remember: "desu" is a grammatical particle in its own right and functions differently from the full verb "de aru".