Personally I think the idea of not revealing mum's name is so OP doesn't go and message her directly and get the child in trouble for looking up his dad online/behind her back. well, if the mum has been prepared to give this boy the dad’s name, the dad’s brother’s name, the name of the football team he supports, and then said that he would be in trouble if he ever went looking, that says an awful lot about her, and none of it complimentary.
But the truth is it’s incredibly easy to find out a lot about someone purely from their name.
We recently found out that one of my parents has a half sibling they never knew about. We didn’t contact them, but from their name alone, and even though they have a fairly locked down fb profile I was able to find out:
Their husband’s name
Their other sibling’s name, who is now deceased. What the sibling died from, the children’s names, ages and dates of birth.
Her job and employer. I brought up her linkedin profile and found out how long she had worked there.
And all I had to start with was a name. There is no such thing as anonymity on the internet.
So no. A common brother’s name wouldn’t sell it to me.
I’m afraid that if someone wants to be taken seriously there is a price to pay. And that price is giving out something genuinely identifying such as his mother’s name or failing that, agreeing to a DNA test, although if he’s under 18 he may not be able to do that.
If he’s not prepared to give out one of those things then it’s an absolute no.
This is why I’m so against e.g. the idea of donor conception. Because when the children born of those conceptions goes looking for their biological heritage, they are the ones who have to make the most sacrifices.