You can ask Terra Kendama kindly and they might let you design it but it would cost money. Thats the only one I have found right now Thanks! - Hon
Roots kendama used to let you choose the wood and paint style of a kendama. However, I'm not sure if they have that option anymore Also, sunrise has a dama that comes with markers and stuff so you can draw on the ken or tama. Hope this helps!
I don't know of any companies that offer full custom painted damas, but several individuals and artists are always open to painting something custom!
Just a heads up, Terra Kendama doesn't do custom painting. You're just thinking of some events that Sourmash has painted at
Definitely @Kayadama ! Once he has the time he will make a master piece. Haven't had one of his damas yet but have heard amazing things and they look soooooooooo good.
The closest thing that you'll come to what you're looking for is probably kaya, but a sort of alternative would be like RWB where you can choose tama and ken-only options in different woods
Roots Kendamas has a design your own kendama option where you can make your own color way and they will try their best to make it and you can choose woods too.they may have took it off the site but I'm sure it will come back just needs more people to buy it because I didn't see much people doing it. Link Here----->http://www.rootskendama.com/collections/design-a-kendama