Disclaimer: I am not a lawyer. There is a concept in copyright law called "fair use". This means that you can use short quotes from someone else's copyrighted work without permission. See here from the US Copyright office Link.
Special deference is given to use for educational or literary purposes. Like one scholar can quote another to offer his own views on the others ideas. Or a critic can quote from someone else's work when giving a review. Neither of those apply to you, so you have to go to the next tier.
Next thing is how much of the work you quote. If you quote the entire song you are on much more dangerous ground that if you quote one line.
For non-educational use, the key criterion is: do you affect the market for the original work. If, for example, someone else wrote a poem, and you copy his entire poem into your book, then anyone who buys your book has no reason to buy a copy of his poem from him. You've hurt his potential sales. He would almost certainly win a copyright suit. A song is a little different, as someone could read the lyrics and say, Hey, I'd really like to hear the music that goes with this, and it might actually help his sales. But I wouldn't count on that.
Short answer: Don't quote the entire lyrics of a song without permission. You can probably get away with a line or two as fair use. Leave it at that.
The title of the song and the name of the group are not and cannot be copyrighted, but they can be trademarked, which is a whole different thing. Basically there the key is that you cannot attempt to confuse potential customers. If you decided to form your own band and called it Rage Again With Machines or Rage Against the Marines, you'd be setting yourself up for a trademark lawsuit. If it's an obvious parody, you can get away with it, but not if you are just trying to trick people into thinking you are the famous group. It's safe to use someone else's trademark in your book as long as you use it correctly and you use it to refer to them. Lots of books mention a character "drinking a Coke" or "driving his Chevy". You do have to be careful to use a trademark correctly. Like Coca Cola's lawyers used to regularly send letters to writers who wrote "coke" with a small-c, and they threatened restaurants with lawsuits if someone ordered a Coke and they gave him some other brand. (So that now, if you order a Coke in a restaurant in the U.S. and they don't serve Coca Cola products, they are likely to say, "Is Pepsi okay?" or something similar.)
Just BTW: I don't know the audience for your book. Are you sure that every reader will be familiar with this particular group and this particular song? Personally, I've only vaguely heard of the group and I've never heard of that particular song. Maybe I'm not the audience for your book. I've often seen writers fall into the trap of thinking that everyone thinks and acts just like them. Like "Everybody reads this magazine" or "Everybody is in favor of X", when the reality is more like "I and my close friends do this". Of course if it doesn't really matter, if you're just trying to set a mood that the character is singing along to a popular song, and exactly what the song is doesn't make much difference, readers who don't know will just say "whatever" and read on, then no problem. But if you're expecting readers to know the lyrics and this is important to the story, then readers who DON'T know the lyrics will be missing out.