After you did find all your players currently, create a separate sheet, p.e. Players.

In this sheet, fill a table with columns p.e. ForeName, LastName, and maybe FullName too;
Enter names of all players into table;
Define this table as Table (Insert>Table, Check 'My table has headers'). Give a meaningful name to defined table, p.e. tPlayers;
Into FullName column of tPlayers, enter the formulaCreate a named range, p.e. lPlayers (Formulas>Name Manager, New), Into RefersTo enter the formula or ;
On sheet with your current table, select all cells where names must be entered. From menu, select Data>Data Validation. Select 'From List', and enter the formula .

Now when you select a cell for players in your table, the cell works like a combo box - you can select a player from table tPlayer. And you can't enter any player name which was not registered before in table tPlayer (and typos are restricted too).

The order the players are listed for selection is determined with order, players are sorted with in table tPlayers.

And you don't need to search the whole entry table anymore, to find out is the player registered before or not.