Why is :Destroy() not working on an Accessory?

hat is defined as the hats name, possibly? so make variable ~~~~~~~~~~~~~~~~~ local hat = char:FindFirstChild(currentHat). ~~~~~~~~~~~~~~~~~ I don't think you need to put the .Name ?

This script should work, the problem is since you're just using an if statement and not a listening event it needs to constantly run to check the value

while true do
    wait()
    if script.Parent.Text == "Unequip" and check == true then
            local hat = char:FindFirstChild(currentHat.Name)
            if hat then
                print(hat.Name)
                hat:Destroy()
                script.Parent.Text = "Equip"
                script.Parent.BackgroundColor3 = Color3.new(0, 211, 0)
        end
    end
end

WARNING: Using many while true do loops in succession can cause server lag, I would strongly advise you to switch this from a Script to a Local Script. Local Scripts have GUI event listeners and are strongly advised. You can use the .Activated event in succession with a remote event to solve this. You will need multiple scripts, firstly a Local Script which is a child of the GUI button:

local ReplicatedStorage = game:GetService("ReplicatedStorage")
local remoteEvent = ReplicatedStorage:WaitForChild("removeHat")

local Players = game:GetService("Players")
local Player = Players.LocalPlayer
local char = Player.Character
local button = script.Parent

local function click()
    if button.Text == "Unequip" then
            local hat = char:FindFirstChild(currentHat.Name) --Dont forget to add current var
            if hat then
                print(hat.Name)
                removeHat:FireServer(hat)
                script.Parent.Text = "Equip"
                script.Parent.BackgroundColor3 = Color3.new(0, 211, 0)
        end
    end
end
button.Activated:Connect(click)

In ReplicatedStorage add a RemoteEvent and name it removeHat

Finally, put this in a normal Script object in the ServerScriptService:

local ReplicatedStorage = game:GetService("ReplicatedStorage")
local remoteEvent = ReplicatedStorage:WaitForChild("removeHat")

remoteEvent.OnServerEvent:Connect(function(hat)
    hat:Destroy()
end)

I really hope this helped, if it did you can mark it as the answer. Also don't forget to comment if there's any errors, good luck!