Star Trek named (customizable) coaster set

I have a relatively large family, and when my adult kids come over, with their significant others, people tend to lose track of whose drink belongs to whom (especially after we have all had a few). So, I decided to make a named coaster for everyone. I started with simple round coasters with odd lettering, but then I wanted to make some coasters for guests. The word "guest" just isn't funny. So, I moved to "extra", which lead me to "not worthy of a name", which lead me to "expendable", which lead me to "Red Shirt"...Perfect.

Then I figured since I am using a Star Trek reference for the guests, I should just go with a full-blown Star Trek coaster set.

After a few iterations I landed on a modified Starfleet Command logo (for the growed ups), and a modified Starfleet Academy logo for the grandkids.
Each coaster measures 90mm in diameter and 4.5mm thick.

Then I needed a holder for all the coasters. Where better to hold your Star Trek coasters than a space station. Ok space d