Every current US Destroyer, the Arleigh Burke classes, all 62 in their several variants, are 8300-9800 tons. So all would be more like a WWII light cruiser. Before them the Spruance class were 8000 tons. This new one is pretty big indeed, but the trend is consistent.
I guess they could just call it a cruiser, or a ship of the line, or a battleship, and be done with it. It’s not like the WWII functional classes really apply anymore.
I’d lean towards calling it a Panzerschiff. But there’s not a chance in Hell of that happening.