You can test for when a player kills an entity and add a point to a
dummy score that will be displayed:
execute as @a if score @s Cre matches 1 run scoreboard players add <player> TK 1
Cre has the score
minecraft.killed:minecraft.creeper and will detect when a player kills a creeper.
TK is the displayed score. The command adds 1 to the
TK score and this will show how many creepers the players have killed, or how many points a player has.
<player> area you can add a custom name so that it will say something like,
CreepersKilled, but you won't be able to see which player it belongs to.
By adding a real player in the
<player> area you can test for specific players using their names, but this requires that you set up commands for every player separately.
And there is no way to display scores to only one player unless you use a plugin (and maybe a datapack).
As I said above it can be done if you know all players that will play and set up dedicated commands for each and every one. Otherwise, I would recommend using a plugin, can't give any suggestions on plugins sorry.