Frame Chests and Illusion Chests do not keep and display their custom name after placing it into the world like vanilla inventories do. (Version 0.3.6)

It's working now, finally!!! I'll release it with the next major update :)
Thanks for reporting and sorry for not responding, I was very busy with my studies...
Regards, Manu

Fixed with 0.4.0

Again, thanks for reporting! :)