As @peer said, you can use a regex in a while loop.
There is no way to do it with input command.
Exemple of code:
import re
playerName = '_'
while(not re.match("^[A-Za-z0-9]*$", playerName)):
playerName = input('Please enter a player name (Only letters and numbers)')
print("PlayerName: ", playerName)
EDIT
As @Joe Ferndz wrote in comment, you can use isalnum() method to check if your playerName is alphanumeric, so you don't even need to use regex
playerName = '_'
while(not playerName.isalnum()):
playerName = input('Please enter a player name (Only letters and numbers)')
print("PlayerName: ", playerName)