Awesome McCool Name: Marina means "of the sea", Lambrini means "bright" or "shining", and Diamandis (of course) means "diamonds." Meaning her full name can be translated as "shining diamonds of the sea."
Critical Backlash/Critical Dissonance: Electra Heart was negatively reviewed by critics, but it was well received by fans, resulting in the album charting #1 in the UK and Ireland.
Averted with "Froot" which was both commercially and critically successful (her highest selling album to date in the United States). One critic even compared the album to True Blue era Madonna.
Ear Worm: "Oh No!" can get inside your head and wind up unable to break out.
"Primadonna" and "Homewrecker" too.
"I'm Miss Sugar Pink, liquor liquor lips, I'm gonna be your bubblegum bitch."
I don't want to be Blue anymore. BBBBLLUUUUUUEEEEEEEEEEEEEEEEE
With Lana Del Rey. To the point on Tumblr users often associate them with each other.
Melanie Martinez fans are becoming a part of the mix too. It helps many fans enjoy all three singers.
Germans Love David Hasselhoff: Marina has commented that her fans in the UK took the "Electra Heart" album, and particularly it's opening song, "Bubblegum Bitch" very seriously. In contrast, her American fans better understood the irony she wanted to get across.
Growing the Beard: Arguably with Froot, with it's more nuanced and stylistically varied production as well as an overall more contemplative and emotional tone- in contrast to the more bluntly satirical The Family Jewels and Electra Heart.
LGBT Fanbase: Given her elaborate art/camp style and her pointed subversion of stereotypical gender tropes, it's not surprising she has grown a large international following.
Memetic Mutation: At least in-fandom: "Oh my God, you look just like Shakira! No no, you're Catherine Zeta! Actually, my name's Marina."