Alien ship classes can be displayed by the phonetic alphabet tables, as it was in NATO naval practice ("Alpha class", "Bravo class", ... - list ordered by the time of first contact with this class).
That's easy, RP-cool, handy to memorize, and doesn't tell you any unnecessary information about alien designs.
More of that, this table can be selected from the list (NATO/ITU-R RTPA, Greek PA, Hebrew PA, LAPD PA), or even written by player himself.
Another solution is to use first names from officer names table, filtered by the main name scheme of that empire.
It will give more length, so when you contact more classes of that empire, than there are words in this phonetic alphabet - there will be less need with names list to use suffixes (like "Alpha-2" or "Alpha II" classes - those can be misunderstood by new players as succeed classes or blocks of one class).
But it can be less handy, because there are some very similar or even duplicated names in those name lists.
I'd like to see first variant (RTPA list) - smth like "Klingon Alpha class" ... "Klingon Victor class" ... "Klingon Alpha-2 class" ... - but only if it will be some personalization possibility.
If it will be hardcoded algorithm - than I'd prefer last variant (officer first names list of empire scheme).