He pronounced it mew ler. It took me a while to make this change with Robert Muller.

I wonder if it's a regional thing going back to the ancestors or something.

And I know that doesn't address your comment specifically.. I'm just thinking out loud here

Germans would pronounce it more like Mewler.

Of course Bob Mueller can pronounce it any way he prefers.

We had family friends when I was growing up named the Muellers and they pronounced it Mew-ler.

It also took me a while to get used to saying Mull-er, I think because I mostly read news instead of watching/listening to it.

It depends on the locale. For example:
https://www.kut.org/post/ok-whats-right-way-pronounce-mueller

Unless you hear him speak say his name you wouldn't know.

And even then, you might not see that there's much of a difference, depending on how much you think it really matters which variant you use.

... nobody has ever heard him speak his name.

I'm guessing it should rhyme with puller or fuller.

But if it rhymes with "duller" when he says it, so be it.

how to pronounce their name then they should change it to a word not exceeding 4 letters. Either that or leave me the hell alone!