Kestrelcollector / Kestrelhoarder (Namecollector / Namehoarder)
Seeing as collecting and hoarding terms tend to have bird-related names and noting that namecollector doesn't have any yet, I propose to you: Kestrelcollector and Kestrelhoarder as alternative terms to namecollector and namehoarder.
That's good question :D I chose kestrel because in german this bird has least 7 different names. In english I also found at least 7 names for it. So you could argue that it's collecting names - just not consciously and of it's own will.
So I'd say it's a decent pick for a term related to name collecting. :D
And I'll throw a bird-y flag design on top of the proposal pile :D
It's based of the existing orange yellow namecollector / namehoarder flags and the rhombi hoarder / collector flags.
Random side fact:
While researching birds, I stumbled across this gem on wikipedia: "Archaic names for the kestrel include windhover and windfucker, due to its habit of beating the wind (hovering in air)." :'D (https://en.wikipedia.org/wiki/Common_kestrel)