Our son is called Matthew.
I found this in Longman. Exemplifying what word?
Is it as natural as Our son's name is Matthew? Yes.
What about Our son is named Matthew? That's less natural.
Hmm. I wouldn't say your dialogues are unnatural (I think we need to clarify again what 'natural' means to us), but that doesn't seem to me like an ideal example context for either utterance. Don't you think we'd be more likely to hear:As far as the first two go, there might be a context in which I would use one or the other, but there are plenty of contexts in which I would them interchangeably.
Helen: That's a nice photo. Are they your kids?
Tom: Yes. My son's name is Matthew and my daughter's name is Alice.
Helen: That's a nice photo. Are they your kids?
Tom: Yes. My son's called Matthew and my daughter's called Alice.
I can see no reason why anyone would choose one over the other in that dialogue, other than simply their personal way of speaking.
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