I'm currently describing a scene of a girl listening to music. My question is, should I say what singer is she listening to? Or I better skip that part and and say something like "she sat on her bed while one of the songs of her favourite singer was being played"?
Use Details To Grab Readers
A guy drove down the road in his car and a thing happened.
Walt Chambers, sat behind the wheel of his 1968 Camaro and revved the engine waiting for the red light to change. He looked right, out the passenger window and saw a green Mustang sitting in the lane next to him.
Details are one of the reasons people read fiction.
Reason You May Decide To Include Artist Names
Most likely the artist the character is listening to will give the reader an idea of who the character is. It will add to the reader's understanding who the character is by showing what they like.
Pop Culture References Can Date A Book/Story
The only problem you might have is that pop culture references can become stale over time as artists become distant memories and could later confuse people if the artist is no longer known.
Ultimately: Your Choice Is Your Style
In the end, whether you provide the specific detail of the artist your character is listening to is your style and your voice coming through. For an example of someone who drops references to music like this all the time and builds his stories on it, check out Nick Hornby Hi Fidelity - amazon link.
In general, I'd avoid naming a specific musician in a causal reference like, "When Sally got home, she sat on her bed and listened to X".
(a) Popular musicians come and go pretty quickly, and naming one is likely to make your story sound dated very rapidly. Singers who were top of the charts just 10 or 15 years ago are often unknown to modern teenagers. Just recently I looked up on YouTube some singers who were popular when I was a young man in the 1980s, and my college-aged son had never heard of any of them. If someone reads your story 10 or 20 years ago, they may well think, "What? A teenager was listening to this grandpa music? Is this kid some kind of extreme traditionalist? A student of music history?"
(b) Musicians are often unknown to people not interested in their genre. Country music fans tend to be unfamiliar with rappers and vice versa, etc. An unfamiliar name is likely to just be distracting, as the reader wonders who it is.
(c) Similarly, people who are not particularly interested in music may not know a name even if the musician is fairly popular.
If the nature of the music doesn't matter, I'd just say, "listening to her favorite singer" or something generic. If the type of music is important in establishing the character, you can describe the music. "She was listening to raucous heavy metal" or "listening to mellow, sentimental love songs" or whatever.
If there's some reason why the particular singer is important -- like, I don't know, an important plot element is how she sees parallels between her life and the lyrics of his songs or something, where you have to go into detail for the story to make sense and be interesting -- that would be different.
BTW In general I agree with SaberWriter that details are important. No one wants to read a story that says, "Some guy did stuff and then other things happened. The end." But pop culture references are tricky for reasons I outlined above. I'd be more inclined to describe the kind of music then to name a contemporary singer.
Oh, I should say that if it's a musician who is very widely known and has been for many years, that's a different category. A reference to Beethoven or Elvis (whew, that's an odd pairing) would likely be recognized by almost any American anyway, and I think it's a fair bet that they'll be remembered for many years to come.
Do what serves your story best. If the artists are relevant, then mention them. In most cases, though, the artists are not necessary. Keep in mind that readers might not even know the artists.
The genre might be useful, though. If her playlist is unique in some way it might contribute to our understanding of her: 70s punk or 60s easy listening or Tuvan throat singing.
Best is to write your best draft and have your readers look it over with a critical eye.
So there are three things I take into consideration: Is the singer going to be a part of the story? If not than I try to look for songs that are 5-10 years older than the current setting as they are still period specific but it's not too specific that it was clear you were writing in a specific year. If it's an period piece, make sure you get some of the most identifiable songs of the decade (no late 90s piece is complete without "All Star" by Smash Mouth, and you can tell it's the '40s cause Intro to "Swing Swing Swing" is playing loudly in the Club). Other options are songs and bands that have withstood the test of time, The Beatles, Rolling Stone, Ozzie Osborn, Michael Jackson, Elvis, Bon Jovie, Weird Al (don't laugh... the man's one of three artists to Have a Platinum Album in every Decade since the 80s... Michael Jackson and Madonna being the other two).
If the Band is going to appear at all in the story and interact with the character or be in the same room as her, than the band should be a fictional band but you can get some great commentary against similar genre artists. For example, the Mockumentary film "Spinal Tap" was making fun of 80s Rock Band excesses and several of the funnier moments were pretty much lifted from actual stories from real life bands... and others were just the over the top excesses of bands of the era. Popular targets are Female Pop acts (almost always solo, as Girl Bands never caught on like Boy Bands) and most started as a child actress who is now trying to break her more wholesome image (Usually by saying "She was working for the Mouse" as Disney Alumn actresses tend to go big in their music careers. Both Britney Spears and Miley Cyrus were known for being Disney Channel celebs before their major singing careers). Boy Bands and Solo Tween heart throbs are also easy targets as they tend to be very corporate and reviled by anyone who isn't a girl in a couple of steps in age from 12. There's also a formula of the vein of "The Shy One, the Cute One, The Hot One, The Bad Boy, and the Big Brother"). Oddly, Americans seem to be less impressed with the genre than the Brits. In the States, it comes and goes over time, while there hasn't not been a hot boyband in the UK since the 70s.
An in series band can be more flexible as it allows the group to interact with protagonists from time to time and make commentaries on various genres of music without actually having to deal with real world history.