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Um, obviously yes - you can't reuse existing ship design names. I'm not sure I understood the question, though:

If you meant "Do I give them actual names instead of something like Fast Medium Ship m1" - well, that depends on how creative I'm feeling that game.

If you meant "Do I name individual ships", that's a long post I won't go into until I'm sure that's what you meant.

In that case, of course!  Creative naming is a weak point of mine, so I usually go with a theme such as a certain mythology or fictional reference or the like.

How I name a model usually depends on the race. For Humans, I often go for mythological names (especially really obscure ones that are almost never used, like Cyhyraeth, or Poqhiraj) from many different cultures, not just Classical mythology, to really give the feel of a truly United Earth.

For Arceans, I'd go with abstract concepts, like Honour, Conduct, and Noblesse Oblige. Other things like documents, such as Contract, Oath, Dictate, would work too. The latter makes sense, to me, at least because of the idea of unbiased justice makes sense with a race dedicated to both honour and neutrality.

For Iconians, I use words like New Dawn, Rising Sun, Resurgence, Glorious Return, and Reclamation, all to point to the fact that this race is rising from the ashes, and that their new ascendance is only beginning.

Usually I play my custom races though, and they all have 'rules' of their own, but I thought sharing these thought would help. 

For humans i use historical figures names - Magellen - Columbus - Attila - Temujin - Washington, etc.

For the other races i some times make up gibberish, other times its random mythological or just totaly random.