I have everything listed as "Ke$ha" sans Lover, but when she releases her album, I'll start labelling everything as "Kesha". I do the same thing with Lana Del Rey, as well. She's listed as Lana Del Rey, Lana Del Ray, Lizzy Grant, Lizzy Grant & The Phenomena, Elizabeth Woolridge, May Jailer and etc. in my libraries.
Mess.
All of released stuff for me is still listed as Ke$ha but everything else is listed as Kesha and it doesn't separate the two into different artists for me so