I don't think there is a way to check? I'll be honest I think the dye system in the game is a bit weak (I wish dye preview was a thing). What I personally do is (with mods) I have a dye bag in my inventory and put a bottle of each dye that I am currently using on any outfits that my character has so it's not too tedious trying to figure out which dye I used since I tend to stick to a select few.
If the item you're using is a vanilla outfit, you might be able to search around online and find a dye chart with said outfit to see if you can quickly find out that way.
