If that's exactly what your text says, it's wrong.
Mary has two children whose names are John and Tom.
This may refer to a situation in which Mary has more than those two children, and that may be evident in context; but by itself the sentence does not entail (require) that interpretation. For instance:
A: Hey, I've found a couple of identical backpacks with the names 'John' and 'Tom' written inside. Do any of our school's mothers have children named John and Tom?
B: Well, there's Mary. She has thirteen children, and I'm pretty sure she has two whose names are John and Tom.
Your second sentence, "I have a son who is interested in music", is also ambiguous: it might be used of either an only son or one of many sons.
A restrictive relative clause is just like any other adjectival—a frank adjective like red for instance. If you say "I have a red sock", this does not imply that you have no other socks.
Formally, an adjectival restricts the reference of the noun it modifies to specific members of the class which the noun designates: it informs your hearer that you are not talking about just any sock or child or son but about particular entities of that class. But by itself it neither entails nor implies anything about other members of the class.
(Note, by the way, that a non-restrictive relative clause is not an adjectival: it doesn't modify the noun it describes, but asserts a new predication about it.)