I disagree with both Golly and erik_t on the issue of aviation. The USN kept aircraft on board its cruisers till ca. 1950, when the catapults were finally removed and the aviation replaced with helicopters in some cases. The RHN would have great use of fighter/spotter planes operating from their cruisers. The geography and topography of the Aegean and southern Adriatic littoral makes it very hard for radar (especially the kind of primitive type they had in the 1940s) to fully penetrate , due to the numerous islets, islands and mountain ranges being in their way. Thus a 1940s enemy fleet could relatively easily penetrate, say from the West to the East by basically hogging the Greek shorelines. Spotters could effectively aid in the early detection of such operations.
As for names, how 'bout "Vasilefs Romanos I Lekapenos" after the great Byzantine admiral cum Emperor, whose time was a golden era for the Byzantine navy?
The USN still operated in the Atlantic and Pacific, oceans many thousands of kilometers across. Flying across the Med is, oh, about 300.
Completely and utterly different roles. Even if you demand the capability to have aircraft spotting your fire, I have no idea why one wouldn't make this happen with dedicated land units ashore.