gms_highscore_name - GameMaker Server

Usage: gms_highscore_name ( list_id, n )

Description

Returns the n'th name on the given highscorelist. An empty string ("") will be returned when exceeding server_highscore_count.

//Show the first name on highscorelist '1'
var name;
name = gms_highscore_name(1, 0)//first place
show_message("First place: "+name);

is that name of player?

This will return the name of the player, yes.