In Guardians of the Galaxy 2 when Peter has decided to fight Ego and he keeps destroying Ego's body, Ego eventually changes to David Hasselhoff saying something along the lines of:
I simply picked the form that would be most pleasing to you, would you prefer this instead?
As far as I recall Peter had never revealed to Ego that he used to tell people that the Hoff was his dad.
Can Ego read minds? If no, how else did he get this information?
According to the official Marvel comic character page for Ego, under the powers section, it says:
Ego has vast mental powers that allow it to tap into energy sources such as the stars or absorbing other living entities and use that power for itself. It also has extreme telepathic abilities that are effective over interstellar distances.
Thus it would appear that Ego from the MCU should have the ability to read minds, assuming he is like his comic counterpart in that way. The question itself is evidence that he probably can.
The simpler solution is that he overheard Peter and Gamora's discussion before where Peter stated that he used to tell people that the Hoff was his dad. Even if he didn't know what Hasslehoff looked like, either from his own memories, or some sort of cosmic knowledge, Peter is shown to have carried a clipping of Hasslehoff in his wallet, and Ego might have peeked at that.
