Yes, when the noun phrase is the object of a preposition as it is here, it changes into the oblique case. Marked singular masculine nouns like मेरा बेटा change to मेरे बेटे
How can you tell if this is singular oblique or plural oblique, then? Is there a different inflection for plural oblique nouns?
It's based on context. For example, its unlikely that many sons are named Peter, so we can derive that we are only talking about a single son.
I translated it into " The name of my son is Peter." Would this be acceptable?