The MoPac is so named because the freeway overlays the MoPac Railroad. Brandon Kraft writes:
For a good amount of the length of the freeway, the Missouri-Pacific rail line is laid between the main lanes of the freeway on the medians. The freeway was known for having the MoPac lines with it so thus the name stuck.
Texas State Loop 1 / State Highway 1 Guides
The tolled extension of Loop 1 opened on November 1, 2007, extending the state highway north from FM 734 (Parmer Lane) to the new Toll 45 N freeway, west of Interstate 35 and east of U.S. 183 / Toll 183A.