The only people I’ve heard say that they hate Lana Del Rey are also teenage girls.
Creating a stage persona is one of the oldest tricks in Hollywood, and it’s been done by some of the biggest pop stars. The name change in itself is also not uncommon. Rita Hayworth was born Margarita Carmen Cansino; Kid Cudi changed his name from Scott Ramon Seguro Mescudi. Hell, one of the most iconically “authentic” artists, Bob Dylan, was born Robert Zimmerman. Authenticity itself is a construct of the music industry.
Remember when Rivers Cuomo was in that metal band?
Also when Trent Reznor was in that new wave group.
You just try a bunch of things and find what works.