New USS Arizona?

The ship names are just what they give to the various divisions at boot camp.  They represent various Navy ships throughout history.  Go ahead and send your sons letter to the address he gave you - and even if you don't put the actual ship name on there, it will get there.

Here's the link to confirm the mailing address.  Note that they don't even list a ship name.

Mailing address confirmation

The buildings the recruit divisions are housed in are named for ships. There is an address, bldg number, ship number and ship name for all the buildings. The only thing you need to include when addressing your recruits is Ship # and Division #. Even the buildings on the TSC side have ship names attached to them.