How do I grab a player's name and insert it in a script?

Parameter is a very clever way of identifying what actually triggered your events. Here's a example.

script.Parent.ClickDetector.MouseClick:connect(function(Click)--The Parameter can be given any string name you desire e.g "Click"
    print(Click)--This will print out the name of the Player that triggered the touch event
end)

~ UserOnly16Characters Hoped I helped you to answer your question! If you have any further question, don't hesitate to comment below!!

Edited:

script.Parent.ClickDetector.MouseClick:connect(function(Click)
    local Message = Instance.new("Hint",game.Workspace)
    Message.Text = Click.Name.." Has clicked this button"
    wait(3)
    Message:Destroy()
end)