Hi, nope, no drawing of names. I end up seeing quite a few staff members repeatedly........and they are always happy to dine with guests.
So, no I never get an invitation on my door. It is more like chatting with people I know and asking them if they would like to dine together.
I sail solo and it is always nice seeing familiar faces and so in my case, that is how it works (for me). SS, in my opinion is always very welcoming to their guests. Oh, I never book an "upper suite".......just a regular veranda. So, cabin category has nothing to do with it.