star trek - How is Voyager so well known within the Delta Quadrant?

Because:

They say gossip travels faster than warp speed.

-The Doctor, VOY: Someone to Watch Over Me

In seriousness, calccrypto touches on one significant factor: Subspace communications travel faster than Voyager's maximum warp speed (apparently warp 9.9997 (although that statement seems to be uncited, it is consistent that subspace comms are faster than starships), compared to Voyager's top speed of warp 9.975). So in that respect, the Doctor is completely correct -- gossip does travel faster than (a ship at) warp.

The other side of the coin is that, while Voyager does want to get home, they spend a lot of time not doing that. It's not just "getting off course on occasion", although that does of course happen, but it's also that Captain Janeway and her crew are still at heart explorers, and jump at almost any opportunity to meet new cultures, to explore strange new phenomenon, or just to lend a helping hand now and again. To say nothing of the time spent acquiring fresh resources, making repairs, fighting/running from hostile aliens, or giving the warp engines a bit of a breather (maximum warp can only be kept up for so long, and even standard cruising speed isn't indefinite).

Plus, it seems like almost every other episode they're going dozens to hundreds to even thousands of light-years in the wrong direction, just to check out something neat or to respond to a distress beacon. That alone would give their reputation and rumors about their exploits ample time to stay well ahead of them, as every 1 light-year that they back-track is 2 light-years behind where they otherwise would have been!