What are the names, or arguments of the atomic sentence
Max ate a cake
I ate a cake.
First of all, "Max" is definitely a name. But is "cake" a name? And in the second sentence, is "I" a name? I am a bit confused.
"Cake" is an arbitrary name for a food, just as "Max" is an arbitrary name for a person. "I" isn't a name, but a pronoun. It can be replaced with a name (such as Max), but is not a name by itself.