How to find a player without typing their full name in a textbox?

You can use string patterns to accomplish this. All you need to do is loop through all the players in the game and check to see if there is a substring (anchored to the beginning using the ^ anchor) that matches what was given. It may also be convenient to ignore case using the lower method in the string library.

Example assuming you are in the game:

local function getPlayerFromSubstring(substring)
    for _, player in ipairs(game.Players:GetPlayers()) do
        if string.lower(player.Name):match("^"..string.lower(substring)) then
            return player
        end
    end
    return nil
end

print(getPlayerFromSubstring("Magic"))
-- Output: Magicboopoo