How Can I Make It When My Mouse Hovers Over A Player A Gui Comes Up With There Name?

Not sure if you wanted it to display the GUI when the user hovered over their own character or not, but you had the right idea. Also, by default, Mouse.TargetFilter is set to the player's character, meaning the
target would be the object behind the character. Also, next time, please put your code into lua code tags (~~~~~~~~~~~~~~~~~)

local Player = Game.Players.LocalPlayer 
local Mouse = Player:GetMouse()
Mouse.TargetFilter = nil -- Set TargetFilter to nil so it doesn't ignore the character..

Mouse.Move:connect(function() 
	if not Mouse.Target.Parent then return end -- checking if the target's parent is not nil
	
	if Mouse.Target and Mouse.Target.Parent == Player.Character then 
		Player.PlayerGui.ScreenGui.SpecialHoverGui.Text = Player.Name
		Player.PlayerGui.ScreenGui.SpecialHoverGui.Visible = true 
	elseif Mouse.Target and Mouse.Target.Parent ~= Player.Character then 
		Player.PlayerGui.ScreenGui.SpecialHoverGui.Visible = false 
	end
end)