Localscript can't find StringValue?

In my game there is a localscript that assigns the value of a StringValue as the name of the player. The StringValue is stored inside a button, so it has instances in StarterGui and inside the PlayerGui of all players. Here is the code:

script.Parent.PlayerName.Value = game.Players.LocalPlayer.Character.Name

It runs absolutely fine in Roblox Studio, but when I play my game normally through Roblox Player, I receive this error in the developer console:

PlayerName is not a valid member of TextButton

What is causing this?

Since this is in a local script use a WaitForChild as instances do not load immediately on the client. Your code should be:

script.Parent:WaitForChild("PlayerName").Value = game.Players.LocalPlayer.Character.Name