The Valk/Shadow filter is a different part # and is about 3/8" longer than the Triumph/VTX filter. Not sure about the internals of the Valk filter. I can only speculate, but I don't think Honda would have come out with a complete different filter and part # for the VTX filter if the slightly longer existing Valk/Shadow filter would suffice. Possibly they are the same internally if the VTX has oil filter clearance issues and that is why the filter is shorter. Don't know, I've not changed oil on a VTX and seen for myself.
The Triumph T1210444 and the Honda 15410-MFJ-D01 are totally identical except for the printing on the can. They are painted the same black color and are even shrink wrapped in the exact same plastic wrap. Both interchange to the same aftermarket part # in several brands too.
I've been in the auto parts biz for over 30 years and I know a LOT of "farming out" of parts is done. I'll guarantee both Triumph and Honda make none of the filters on any thing they make, it's all farmed out!
It's interesting to note that both Triumph and Honda find that Toyo-Roki makes a high enough quality filter that they will both stamp their names on them. All reviews I've read of Honda branded filters rank them high in quality.
Yep, RR- K&N lists part # KN204 as the oil filter for VTX and R3.