I would guess that stand for Danish Walnut. Are they fairly dark?
I was watching a guy mix in powdered pigments in to various coatings to match shades and could really nail a repair job that way. It would be much harder than just finding similar base wood and stain protection combos.
i stained all my "new" trim in the house with danish walnut. i got it at the "old BIG R" store. i don't know if the new stores carry it or not. good luck finding it .
Right up my alley, I own a cabinet shop. The 3440 is probably the # code from the manufacturer for Danish Walnut, you will probably never know who made the stain because many companys make that color and assign a different # to it.
Your best bet is to take a cabinet door and some sample pieces of your trim to a place like Sherwin Williams and have them match it, stay away from the big box stores for color matches, you will have much better luck with a paint store that professional painters use. There may be a color match charge but it won't be very expensive and will be worth it in the end.