In my case, it would be a moot point since my beer names are like "#424 German Pils".
I'm not nearly to that many batches, but I still get a bit lazy with naming (even though my fiance inspires some pretty great names). I tend to name a recipe that I've been working on for a while (e.g. Pants on Fire, Complete Twaddle, etc) but most of my batches just end up as "Nelson Saison", "Amarillo Saison", "Dry Stout", etc.
I stopped naming my beers some time ago. Not sure when. There are a few batches that I re-brew a lot and those have names. I tend to follow your convention for newer recipes. Small Stout, Quick Saison, etc. If something sticks and I start re-brewing it regularly maybe I'll give it a name.
As to batch #s, I have no idea how many batches I've made. The early years before I kept a log book are lost to time so I guess I will never know. Oh well.
It does seem like gold medal winners should have good names, though.