Muller with umlaut, means miller in German. Miller Muller, potato potahto, ha!
You are familiar with various pronunciations, but during trumps first term the Mueller investigation was mostly pronounced by tv talking heads as 'the Muller Report', rhyming with duller.
Here is a somewhat relevant story from Austin Texas which corroborates my thread premise.
With the glaring exception that this is not the Robert Mueller of this thread. I read somewhere that Muller with umlaut is the most common surname in Germany, so coincidental.
Author does use E instead of U to make his point, I think valid as well as U.
Within the whole article, author does say that Mueller was often pronounced Miller.
Mueller Family Robert Mueller Sr., 1881-1927
"The 'UE' letter sequence is a transliteration of the umlaut," Hinrichs said. "That is a sound English doesn't have ... it's like saying 'E,' but rounding your lips. I will leave it to your listeners to practice it by themselves, but it does not exist in English."
Austin newcomers, he said, will simply pronounce the name as it is spelled.
"It's spelled M-U-E," Hinrichs said. "How does English typically pronounce M-U-E? Well we're going to say [MEW-ler]."
https://www.kut.org/austin/2016-02-19/austin-texas-right-way-pronounce-mueller