I would like to have the ability to specify the type of item I want to go into a bag, similar to the ideas of the "toolbox" and "alchemical kit".
Say I'm doing a whole lot of mining, and maybe not really paying attention to how much I'm mining or where it's going, and I've got a half-dozen slots open in a half-dozen bags; now I've got 36 scattered stacks of beryl and sparkly running rampant through my bags! Arrrrghhhh, +5 minutes spent reorganizing/looking and finding stuff.
So when I go to rename my bag, I'd like another option to appear: "Select the type of goodies you want to keep safe here" followed by such things as "Food; drinks; gems; ore chunks; powders;" &c. Then, any item crafted or otherwise acquired would fly into the appropriate bags, if a slot were available.
Alternatively, just give us more specialized bag options at the vendors! Though, to be honest, I think it would be sleeker in-game to have user-selectable options than a dozen more bag types at the vendor. Less easy to code, though, I'm sure :/