With BK613's find, we're up to 4 variations of the delta patches
4. Rectangle with open right side
With these known parameters:
1. variations only exist on the delta patch,
2. not everyone wears the delta patch - some use a different design that doesn't have room for same variations
3. the delta patch is seen mixed in on other ships that might have different patches
4. character x can switch back and forth between delta patch variations
Then I guess that it is just
a Starfleet patch. The variation is purely cosmetic.
Or it might be a shift patch. It could indicate which of the three shifts the character is currently assigned to. But that wouldn't account for the other patches that don't have room for variations.
So... What sort of identifying/decorative function could we assign to these patches, if they aren't related to the line of work of the character, or his or her rank, or whatnot?
Three symbols for three shifts, perhaps? But it would be a bit weird that we never actually see a shift consisting predominantly of those wearing the appropriate patch.
Three symbols for three pay grades (within each rank)? Scotty might have gotten a raise for the Memory Alpha IT work that was outside his usual field of proficiency...
Three symbols for level of excellence (within each rank), without practical impact on pay or the like? Scotty might be doing better on some weeks than others, but never quite reaches "star grade". It's much easier for those command types who don't have to master actual skills such as impulse engine repair.
Three symbols for time in rank? Scotty would be an old dog at LtCmdr with the highest possible symbol, the sphere, while Kirk would still be a youngster at Captain rank. But when seniority issues arise, even a difference of weeks is of significance, so three levels wouldn't help much.