Here is my idea for Starbase Special Project. It's called Fleet Personnel Quarter.
The purpose of this project is allowing all members of the fleet to have a small quarter on Fleet Starbase. This quarter contains personal bank and a place for trophies. The reason being is that my Jem'Hadar Dreadnaught Carrier has no place for my trophies. The Dev dstahl also mentioned in the game chat that customizing ship interior won't be in a foreseeable future. So, I hope the Dev would still give the option of providing such a place for personal trophies. Some people might argue that I could still place my trophies onboard Fed ships, but I don't want to keep reworking on my skill shortcuts whenever I activate other ships. I don't know whether or not one able to place trophies onboard Klingon ships.
In addition, having personal quarter for each fleet member on a starbase is analogous to having our own bunk bed in a military barrack. So, to me, it is logical to have our own small quarter on a starbase. This personal quarter should be accessible through the turbolift and the owner should be able to invite others to go inside as well.
So, please Dev consider providing a place for personal trophies.