From SmashWiki, the Super Smash Bros. wiki
The Score Display is an optional rule that is available from Super Smash Bros. Melee onward. It is unlocked during Versus Mode by scoring a total of 5,000 KO's in Melee and a total of 200 KOs in Brawl and Super Smash Bros. for Nintendo 3DS; in Super Smash Bros. for Wii U it is available from the beginning. When this rule is switched on, the net score of all combatants in Time and Bonus matches will be displayed on-screen next to their series symbol. Oddly, in Bonus mode, it displays the same score as if it were Time mode, not the amount of Bonus points collected. The Score Display does not appear in Stock and Coin matches. It will always appear when viewing replays of TIme matches.