A space empire, you build one or more (but usually just one) super-something-combat-gigantic-vessel things.
The Empire built two death stars. 
These class of objects are typically called Megastructures - just astro-engineered ones. I'd give them individual unique names just like boats, colonies, planets, and cities have names.
Because Megastructures take so much work to build, it's unlikely there'd be many identical-planned megastructures. How many identical skyscrapers do we have? Few, if any.
Even large boats are usually have only two or three "sister ships", and even then may have modifications unique to each one because new technology gets invented while they are constructed and each one takes so long to build. Boats do have "classifications" to help military quickly group ships mentally into different classes of firepower or different cargo-tonnage. These classes are usually named after one of the first ships (the "lead ship") of that new class. We have Nimitz-class aircraft carriers, and they are named after the Nimitz which was the first of that class.
Rather, each megastructures would be extremely unique and vary greatly in size, shape, blueprints, and so on. The first of a specific size would be given some unique name (i.e. the MS Wiggins), and then later ones of similar size would be called after the original's class (i.e. the MS Monolith might be a Wiggins-class dyson sphere).