Billie Eilish is thrilled to be giving her first Irish interview. One of the year’s brightest musical prospects, her full name is Billie Eilish Pirate Baird… O’Connell. So yes, there’s a connection to the old country. Also, Hot Press pronounces “Eilish” correctly. This is a big deal to the 16-year-old Los Angeleno. She is fed up, at an existential level, of Americans calling her Billie “Eye-lash”.

“I’m Scottish and Irish,” she says. “I can’t tan AT ALL. For years nobody had ‘Eilish’ even in their vocabulary. Literally the other day somebody stopped me in the street to take a picture and he said that his girlfriend’s first name was ‘Eilish’. I was like, ‘Oh my God’. I’m excited to go to Ireland and not be the only one. I like being unique and everything, but I would also like to be somewhere people can pronounce my name correctly.”

Eilish recently turned 16, which might not normally be a big deal in a pop star. A 16-year-old Justin Bieber, for example, made perfect sense (probably more sense than the 23-year-old version). Teenage Taylor Swift singing about high school and mean girls and boys – yes, that added up too.

With Eilish it’s more complex. Her songs feel wise and lived-in to a degree that not only belies her youth – but turns what she does into a high-wire act.

Consider ‘Ocean Eyes’, her biggest hit (to date). The 2016 ballad, in which she likens an unrequited crush to falling off a cliff, is feverish and baroque, in that voguish, Lana del Rey-meets-Lorde way. What it isn’t is throwaway bubblegum – the kind of thing you expect of a teenager from California, home-schooled by actor parents.

“There are people who SO are their age,” she says. “They’re 15 and totally act like a 15-year-old. I have never been that way.”

She signed her first record deal aged 13 and now, three years later, is set to conquer pop. Notably, Eilish was shortlisted for the BBC Sound Of 2018 countdown. Last September, she made her US network television debut, performing ‘Ocean Eyes’ atop a neon Perspex dais on the James Corden show (Zane Lowe popped along to introduce her and dangle a copy of her Don’t Smile At Me EP under Corden’s nose).

The fashion industry loves her, too. She’s rocked her playful hip hop style in the pages of W magazine and Vogue. She has 140,000 Twitter followers, with another half-million on Instagram.

“I’m trying to take it all as if I haven’t been dreaming of it since I was little,” she says. “I think that way I’ll stay the most grounded. I don’t want to take anything for granted. That’s my one wish. If you think about things while you are doing them… well, this is insane. I take in everything as if it’s normal.”

She is, true to the promise she has made to herself, grounded and deprecating in person – not at all the gab-mouthed ingénue. It’s a cliché, but she really does come across as older than her years. She also isn’t terribly interested in fame for its own sake. They all say that of course – but rarely as vehemently.

“I know people who just want to be famous and will do anything to get that fame off you. People just do not understand what the fuck comes with that. Unless you’ve done something horrible and are known for that. If you really want to be known for something good and have people look up to you, then you have to work.”

Eilish grew up in Highland Park, a multicultural north-east Los Angeles enclave perhaps best known for providing the backdrop to Quentin Tarantino’s Reservoir Dogs. Her brother Fineas, five years her senior, acts as Eilish’s collaborator, touring with her and serving as her producer.

The singer has expressed unease in the past with the focus on her age. Yet there’s no getting around it – she was 13 when her earliest demos crossed record company desks in LA. That’s insanely young – and was a subject that came up discussing potential record deals.

“It was definitely part of the conversation,” she says. “I don’t think it could ever not be. I was 13 when we started meeting labels. But I don’t think it’s ever been a reason for something. As in, ‘Oh she’s 13, we have to do this.’ It’s definitely always on people’s minds. On the other hand, people who think you are talented think you are even more talented if you’re really young. It’s almost unfair. I’ll take it.”

With success has come an inevitable distance between Eilish and her friends – who sometimes find it difficult to relate to her life.

“A lot of them get mad at me if I can’t hang out or if I have to take a trip suddenly. Like, they’re really annoyed if I have to go to New York at the last minute. Nobody understands: it’s actually a job. It’s like someone worked in an office and couldn’t hang out with you because they had to do a shift. Just because I’m 16 and it isn’t boring doesn’t mean it’s not a job – it doesn’t mean I’m not working every day, really hard, for something I want.”

The songs she and her brother write are catchy – yet unconventional. Though her music captures the angst, thrill and confusion of adolescence, teen-pop cliche is held at arm’s length. For instance, ‘Bellyache’ – a macabre banger from early 2017 – is told from the perspective of a mass-shooter with a dicky tummy.

“If you listen to any song right now – and there are a few exceptions – but I’ve found they’re all about the same thing. ‘I’m in love with this person, they don’t love me, I’m sad’. Sure you can write about that and feel that way But why not write in a different way? I’m not criticising anyone specifically. I mean, you can go ‘I’m sad’, and that’s fine. But you could turn it around – ‘I just killed a bunch of people and I have a bellyache because of it’.”

Billie Eilish's Don’t Smile At Me EP is out now.