Usernames have a minimum of 3 characters and a maximum of 20 characters. There are 26 letters and 10 numbers to choose from, which gives us a total of 36 characters. The number of possible combinations for usernames is 36^3 + 36^4 + 36^5 + ... + 36^20. That number sums to 13,749,422,954,239,269,326,919,955,860,288.
In other words, we probably won't run out of usernames.
Will the site EVER run out of usernames? It seems like a weird conspiracy but it could happen. As millions open accounts and thousands get closed or closed themselves, the amount of unoriginal usernames skyrocket and soon, we will be left with W392D38sk3 usernames. Plus, some bots could make a bunch of accounts, close them, and continue. If this happens, we will be left with no usernames so if a future GM comes, then will probably not be able to even get through the username system. So, chess.com, take this as a warning before it's too late. As more people want to do chess (thanks to the queens gambit and PogChamps) more usernames will be sucked into the void, and thus, making username supply very short. So, I recommend chess.com make a different system (e.g. FMLarry#69420) to help with the rising amount of people willing to play chess.