The highway and the bridge seem to have several names. The boat access area has a welcome sign, declaring it to be the Loop 360 Boat Ramp. On a map, the highway was labeled 360 and also N Capital of Texas. The highway actually goes about 180° around the west side of downtown.
The bridge is called the Lake Austin bridge with reference to the water under the bridge.The Colorado River formerly flooded often. A series of flood-control dams created a string of lakes. Lake Austin looks like a river to me as it winds through the city. The bridge is officially named the Pennybacker bridge in honor of a TxDOT engineer. The bridge was opened December 3, 1982.
This website tells the history (see items f, g, and h): http://www.texasfreeway.com/Austin/photos/360/360.shtml