What are the numbers after some player's names?

Some players have a number displayed after their names, which shows up on the score board and during fights. The numbers are in little silver discs which appear to get more flashy the higher the number. What do these represent?

This is your prestige level.

Watching this video, it shows the player without any prestige at first at around the 50 second mark, but at the 5:58 mark after they prestige, it shows his name on the leaderboard with a number 1 next to his name indicating he is prestige one. The Wiki for the game also states:

When you enter Prestige, you gain a special icon with a number next to your nickname. The number indicates the Prestige Level. You can activate Prestige Mode up to 10 times.

This number appears to show up next to your name elsewhere as well in the game. You can prestige by viewing the leaderboard and selecting the prestige button in the bottom right once you have beat the last Stage 24.

_{Image from the linked video}