First you need to identify the make and model of the hub. I suspect it's a Specialized branded hub.
Next you just search that make and model on Google and find the drawings or parts lists. Then you try to find that exact component.
Once you have the part you being looking at shopping options.
This can be a long search for a specific part on an older component.
I suspect it's a generic piece that you can't get without buying the whole hub. You can probably find the hub second hand or perhaps new on eBay or Amazon. Also - your LBS may have a bin with this particular part buried in it. Maybe they'll let you dig around for the price of a 12 pack.
It may be easier and faster to just source a new hub of the same dimensions and build up the wheel.
Success! Hit a few LBS and eventually found some in their parts bins. Found that there were many different sizes. The Fatboy is getting close to rolling.
I'm glad you found one that seems to fit. I've usually heard that part referred to as a hub dust seal. And yeah, there are lots of subtly different versions. I said "seems to fit" because maybe it'll do the job, but your broken one appeared to have a hexagonal hole at the outboard side (to match the axle locknut), and the new one doesn't.
Yeah, all the LBS said these were OEM specific. Getting increasingly hard to find. I have a saved search on Fleabay for a combination of 'hub' 'dust' 'seal'.
The ones I did find fit pretty snug against the cone face so it would keep a large portion of water and dirt out. I did pack the cups pretty solid with waterproof grease before I put the bearings back in.