Ke$ha inserted the dollar sign into her name because she was so poor.

Many recording artists choose names having to do with money because they want to sound rich (i.e. Chamillionaire), but Ke$ha wanted to sound clever by being ironic. As you may recall, back when she was featured on the Flo Rida song “Right Round,” she was not credited or paid for the recording. As a result, the artist formerly known as Kesha was dirt poor and “shopping at the dollar store for canned vegetables” despite the fact that she was featured on a number-one single!

In those more desperate times, Ke$ha also broke into Prince's house in order to give him one of her CDs.
(source