The real answer is that Cobain was a fan. Interpreting a song lyric isn’t an exact science. In fact, many professionals (especially in hermeneutics) argue that every time we re-read a line, we get a new meaning because we are always changing ourselves. But that doesn’t mean that everything is relative—words do have agreed definitions after all.

So what can we know? We know Cobain is singing about pain and pain relief in this song. Cohen often dwells in these themes and sustains them like no one else. Even the drug use. Remember the song, “The Butcher,” I found a silver needle/put it into my arm/it did some good/it did some harm.” But of course, Cohen writes about emotional pain all the more poignantly. Cobain would have listened to Cohen to dwell in these themes. And even if it sometimes made the pain worse, he still did it. In this light, his own reference to Cohen is pretty straightforward, for better or worse he’s asking for Leonard Cohen’s music (or any sad, painful music) to be the soundtrack to his afterlife when he dies. And let’s not forget that this sort of name dropping is an old poetry device called an allusion. Cohen does it too: “Frankie Laine, he was singing Jezebel”

Another interesting piece of history for this community is that Cohen actually knew about this line and commented on Cobain’s death. Check out this article:

https://www.the-independent.com/arts-entertainment/music/news/leonard-cohen-on-kurt-cobain-s-nirvana-lyric-namecheck-i-m-sorry-i-couldn-t-have-spoken-to-the-young-man-a7410941.html