The town has no name, it is referred by the name of the fort (which the barracks are a part of) Seawinter Fort, or Seawinter.
There is a warehouse mainly to keep wares that are fragile to the bitter cold. A local tavern, and another that is also a Inn (Seawinter Inn). Other than the local stores (food and tools), there are houses and cottages spread about. The Fort is built rather close to the Hold of the city. The Hold is a small castle where the Lord and Lady of Seawinter reside. A wooden spiked wall incases the closest-knit part of town, Hold, and Fort together to protect against local barbarian tribes.
Hopefully I cleared a few things up for you Soul ^^