Do I have to stay till the end after I die?

To be clear-- no. You get the same Renown if you leave two seconds after you’ve completed the match as you’d get if you spectate the match to the end.

You can leave if you’re dead (in Solos) or if your squad is dead (in Duos) without penalty.

We think we’ve seen cases where it might take a short time for your Renown to update after your match is over, but that’s being investigated and not considered a bug yet.