Our son is called Matthew.

[99bottles]

Our son is called Matthew.

I found this on Longman. Is it as natural as Our son's name is Matthew? What about Our son is named Matthew?

 

[Rover_KE]

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.

 

[99bottles]

It was exemplifying the word call.

I thought it was on Longman because we use on for what is online.

 

[Rover_KE]

I took it to mean in Longman's Dictionary.

 

[emsr2d2]

I would go further than Rover and say that "Our son is called Matthew" is slightly more natural (and more common) than "Our son's name is Matthew". We don't tend to use "named" except in sentences such as "They've named their child Tottenham! Poor kid!"

Regarding the in/on question:
I found it in Longman's Dictionary.
I found it on the Longman's Dictionary website.

 

[jutfrank]

I think this shows that we have different ideas about what 'natural' means.

I would say the difference between these three utterances is use. They would be used in different contexts, to say different things.

 

[emsr2d2]

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.

 

[jutfrank]

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.

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:

Helen: That's a nice photo. Are they your kids?
Tom: Yeah. That's Matthew, and that's Alice.

I'd like to suggest that perhaps the most common and natural way to use called with people's names is when tagging them as extra information, like this:

I've got a sister called Julie and two brothers called Mark and Kieran.
She has a cat called Tiddles.

Otherwise, we tend to reserve using be called for naming things:

What's this called in Spanish?
What's it called when you have the feeling you've done something before?
Do you know what this is called?

We tend to use name when we're focusing solely on people's names, such as when we're introducing ourselves by name:

Hello, everyone. I'm Frank.
Hello, everyone. My name's Frank.
Hello, everyone. I'm called Frank.

 

[Tarheel]

Perhaps:

Our son's name is Michael, but people call him Mike for short.