Text label does not change text?

First of all, make sure it's a localscript (obviously). Secondly, you're using StarterGui. StarterGui immediately replicates everything to the Player.PlayerGui. So you need to manipulate the PlayerGui, not StarterGui. I'll make the changes + some things you should know. (Don't use pause if you're planning to skip the song at the end). Note: You should use a folder and a for loop to optimise your code.

local musicFolder = game.ReplicatedStorage.Musics:GetChildren() --This sounds complicated, but it returns a table full of values, which is your music.
local textLabel = script.Parent.Title --You should parent your TextLabel to the ScreenGui. You can use this or use this: game.Players.LocalPlayer:WaitForChild("PlayerGui").MusicGui.MusicFrame.Title
for i, v in pairs(musicFolder) --This is a special for loop, which loops through tables. This is good for optimisation.
    textLabel.Text = v.Name --This gives the name of the song. You can use this.
    if v:IsA("Sound") then --This is just to check if it's sound.
        v:Play()
        v.Ended:Wait() --This event will only go through when the sound has ended. This is a better alternative than just looking at the timelength.
    end
    wait(1)
end

A player's GUI and a GUI in StarterGui are different. If your script is local, you can do this:

    local MusicFL = game.ReplicatedStorage.Musics
    local MusicText = game.Players.LocalPlayer.PlayerGui.MusicFrame.Title

    ---[Music1] - C418 - Familiar Faces
    ---[Music2] - C418 - Wet Hands
    ---[Music3] - C418 - Chirp
    ---[Music4] - C418 - Wait
    ---[Music5] - Interstellar - No time for caution

    -----------------
    wait(3)
    MusicFL.Music1:Play()
    MusicText.Text = "C418 - Familiar Faces"--- song title change
    wait(119)---length of the music
    MusicFL.Music1:Pause()-- just to make sure
    wait(1)--pause between songs
    MusicFL.Music2:Play()
    MusicText.Text = "C418 - Wet Hands"
    wait(90)
    MusicFL.Music2:Pause()
    wait(1)
    MusicFL.Music3:Play()
    MusicText.Text = "C418 - Chirp"
    wait(198)
    MusicFL.Music3:Pause()
    wait(1)
    MusicFL.Music4:Play()
    MusicText.Text = "C418 - Wait"
    wait(238)
    MusicFL.Music4:Pause()
    wait(1)
    MusicFL.Music5:Play()
    MusicText.Text = "Interstellar - No time for caution"
    wait(248)
    print("Test")