If you're building a culture from scratch, and whatever narration is not based on a human perspective then it would make sense to come up with original classifications. Be a handy way to illustrate the social and cultural differences from the reader's human-centric viewpoint. I'm sure that there's a proper word for "human-centric", but I can't recall what it is...
As for categories of ships though, I expect that unless it's a truly and utterly alien race, with utterly alien technology, (Borg Cubes, Hive Ships, etc) then you'll always have some equivalent in categories of ships if not names for those categories. Capital ships take more time and resources to build and crew, so you wouldn't waste them on routine patrols, destroyers and cruisers are vastly cheaper so you'd build swarms of them you could use to screen your expensive capital ships as well as smaller, routine missions. Your systems/planets/colonies with a lighter industrial base might not be able to produce anything heavy, but they can free up the big shipyards by taking up the slack in light units while the more industrialized locals focus on the big stuff that only they can build efficiently.
This is of course assuming that the story's universe is not a super-science post-scarcity setting with unlimited resources, manpower, training, logistic capacity, all that jazz... I'm thinking in terms more like BSG, B5, etc.
As for battlecruisers, I've seen some SF where they were a good idea. Basically long range, missile platforms that could be deployed and positioned rapidly to put fire where it's needed. They were cheaper, lighter on crewing demands, and had throw weight approaching that of the big heavy sluggers, but not the armor so they had to keep at a distance. Basically the same way modern, self-propelled artillery works. Keep it safe, it's a rain of unholy death, but toe to toe, it's breakfast.
What really bugs me is when someone has a "destroyer" that's going toe to toe with a heavy cruiser, dreadnought, etc because the writer never bothered to look up even the basics of ship classes. It's like the ground-warfare version of thinking a platoon can handle a division or corp. (Barring of course a ridiculous technological advantage. The US's old Spruance class destroyers, the last of which was decommissioned a few years ago, would have had no difficulty butchering both the Bismark and Tirpitz at the same time without mussing it's metaphorical hair.)
