What is the ruling on changing an ugly name to a beautiful one under Libyan law, which prohibits such changes for those over ten years of age?

The Prophet commanded improving names due to their psychological impact on the named person, and he informed that people will be called on the Day of Resurrection by their names and their fathers' names, so names should be improved. If you cannot change your name which causes you embarrassment, you can adopt a name or a kunya by which you are called among your family and acquaintances, while the old name remains for official papers. This is a possible solution if the law prevents changing names. If you cannot do any of that, then you must be patient and seek reward from Allah, and improve yourself through piety towards Allah and the noble ethics of Islam. This will cover any deficiency and conceal any flaw, so do not pay attention to people's talk and comments.