Torso is not a valid member of Model "Workspace.TommyHArden" ?

Easy fix.

There are 2 ways of doing this.

You could:

A) Wait for the torso:

local UserInputService = game:service("UserInputService")

function scanInStorage(placeToScan)
    for _, Object in pairs(placeToScan:GetChildren()) do
        local Plr = game.Players.LocalPlayer
        local Part = Object.Radius
        local Distance = 7

        local UI = Object["Display Part"].BillboardGui
        local Split = string.split(Object.Name, "-")
        local Torso = Plr.Character:WaitForChild('Torso')

        UI.Frame.Regiment.Text = Split[1]

        if (Torso.Position - Part.Position).Magnitude <= Distance then
                UserInputService.InputBegan:Connect(
                    function(Input, GameProcessedEvent)
                        if Input.UserInputType == Enum.UserInputType.Keyboard then
                            if Input.KeyCode == Enum.KeyCode.E then
                                local Remote = game.ReplicatedStorage.Remotes.equipUniform

                                local Shirt = Object.Shirt.ShirtTemplate
                                local Pants = Object.Pants.PantsTemplate

                                wait()
                                Remote:FireServer(Plr, Shirt, Pants)
                            end
                        end
                    end)


            end
    end
end
scanInStorage(game.Workspace.UniformHolder)

B) Use a repeat loop:

local UserInputService = game:service("UserInputService")

function scanInStorage(placeToScan)
    for _, Object in pairs(placeToScan:GetChildren()) do
        local Plr = game.Players.LocalPlayer
        local Part = Object.Radius
        local Distance = 7

        local UI = Object["Display Part"].BillboardGui
        local Split = string.split(Object.Name, "-")
	repeat wait() until Plr.Character:FindFirstChild('Torso')
        local Torso = Plr.Character.Torso
        UI.Frame.Regiment.Text = Split[1]

        if (Torso.Position - Part.Position).Magnitude <= Distance then
                UserInputService.InputBegan:Connect(
                    function(Input, GameProcessedEvent)
                        if Input.UserInputType == Enum.UserInputType.Keyboard then
                            if Input.KeyCode == Enum.KeyCode.E then
                                local Remote = game.ReplicatedStorage.Remotes.equipUniform

                                local Shirt = Object.Shirt.ShirtTemplate
                                local Pants = Object.Pants.PantsTemplate

                                wait()
                                Remote:FireServer(Plr, Shirt, Pants)
                            end
                        end
                    end)


            end
    end
end
scanInStorage(game.Workspace.UniformHolder)