It should be noted that one is allowed to change the display name at will. (This has caused some problems; I have seen the downside of being impersonated in this way.) Indeed, many of the display components of the platform are meant to be configurable.
Gerhard "Let Us All Become Andru" Paseman, 2020.07.10.
MathOverflow has been part of the Stack Exchange network for a very long time, and the Stack Exchange network doesn't enforce this. (I'm not sure how it was back in the days.)
Just as in real life, several people can go by the same first and last name. This usually doesn't cause any problem; it only gets confusing when they interact (but that can be funny ...