Unfortunately, it is not possible to change or modify Skype Usernames. I think such restriction is not only employed by Skype but by other online services as well. Moreover, users can change their Display Name (or Full Name) by going to the Edit Your Profile Page. This is what will also be displayed on the other party when you call them or send them a message.
Yet, if you really need to use a certain username. You may need to create a new account. Users can have more than one account and can even register the same information and email address in the new account/s (but a different email address in each accounts is more advisable).
Moreover, if in case you consider to create a new account and have no intentions to use the old or original one. please click here for more suggestions or advice.