So, I have read about this story on multiple occasions in a day-to-day-calendar called "Things not listed in encyclopedias" that's actually aimed at children, which I read while breakfast. However, no sources are given. Once, a German comedian told it too.
The story goes like this:
When Max Planck discovered the effects of quantum physics for which he later got a Nobel price, he traveled through Germany and gave public speeches about it. Cars were new back then and so -- lacking a driver license and a car -- he got a driver, who would sit in the audience, listening to his talk over and over again, until he knew everything by heart.
They figured out that nobody knew how Planck actually looked like, and started to play a joke where the driver would give the speech, while Planck himself would sit in the audience with the driver's cap.
The driver knew most things by heart and also most answers to the most common questions.
Once, when giving a talk in Munich, the driver was presented a question he never heard before and said "I would've never thought that someone from the University in Munich would ask such a trivial question. My driver can answer this."
Does this story have any authenticity?
Nein, I'm afraid.
First of all — this is a pretty common urban legend with different scientific geniuses swapped in for Planck (the most common variant I have seen is with Einstein, but as Snopes points out, it is an old Jewish joke that can be adapted to any sort of chauffeur vs. brains situation, whether a scientist, a Rabbi, the Pope, whatever).
Second, this is really not Planck's personality at all — he was famously a pretty serious and somber guy on the whole (even before his son was executed for attempting to assassinate Hitler!), especially by the time his work on the quanta was seen as a big deal (he would have been 47 when it really started to take off in the wake of Einstein's 1905 paper on the photoelectric effect, which showed that the quanta was not just a neat math trick but a real physical entity).
Third, the kind of audiences that would attend a talk by Planck (or Einstein, or any other Nobel Physicist) probably would have had included people in it who knew what he looked like — photographs and newspapers existed before 1905, and these communities of scientists were quite international by the early 20th century (I wonder if changing it to Planck, rather than Einstein, is an attempt to make it slightly dorkier and slightly more plausible, since far people — then and now — would have recognized Max Planck from a photo than they would the iconic Albert Einstein).
Anyway, an amusing-enough joke, but not to be taken historically seriously.