Will any named NPC trader turn your level 3 emporium into a level 4? Or do you need to assign a specific named NCP's to each emporium type?

No, most traders are specialized, Rylee is a trader, so she can only improve trading posts, Anne Hargraves is a seamtress, so she will improve the clothing emporium.. Certain traders with names are false traders like the Vaul Tech Rep, he can't improve any post.

If you put him in a general store he sells one piece of legendary armour.

He also sells a lot more junk then normal. If He's a false trader who can't improve any post then so is Rylee

Is there a list of which named NPC's enable specific emporiums become lvl 4?

Yes, he does that but he doesn't improve the store to level 4. He's like a pseudo one.

I'm not sure what you're expecting to have happen when you assign them to the store. It doesn't physically change, but those "level 4" traders offer a piece of legendary equipment and an overall better selection than a standard Settler would. The Vault Tec Rep included.

As far as i know hes general store trader same as Rayle and Holt Combes, all other emporiums only have 1 NPC avilable for them(for the lvl 4 upgrade).