Yes, Cenaculum is an attic room, an upstairs dinning room.
I don't know why they had upstairs dinning room, in Ancient Rome. No idea. (Edit: it was the upstairs dinning room for the slaves and the inferior class people of the household)
Triclinium seems better and more general, than the particular case of dinning rooms in attics or upstairs, even if it was a Roman thing.
In this case, caenaculum should remain untranslated, as it doesn't exist in modern culture, or translated by "upper dining room" or something like that.
You may be thinking of the scene in Acts 1:13 et cum introissent in cenaculum ascenderunt (καὶ ὅτε εἰσῆλθον, εἰς τὸ ὑπερῷον ἀνέβησαν). The last supper texts refer to a τὸ κατάλυμα, which in the Vg is diversorium (lodging place, inn--so also Luke 2:7) in Luke 22:11 but refectio in Mark 14:14. Just FYI. The cenaculum may imply the upper level of tenement housing where the poor people lived in cramped conditions vulnerable to fire.
Triclinium is for the elite, as pye20 notes below. The vast majority of people lived in cramped tenement housing and didn't have a triclinium. To get invited to triclinium dining you had to be an important client and a patron in your own right within the rigid social hierarchy of the patron-client system. For the few who were invited, there was a pecking order about which couch to lie down on (recline) during the meal or symposium.