"Soler Hall," the name of the school where John and Aleyn are studying, is actually "King's Hall," a college that was started by a society of scholars founded by Edward II. Later on it was merged with Trinity Hall, a college of Cambridge. The name "Soler" refers to the number of rooms with windows admitting sunlight, which were called "solars" at this time period. (Source: Riverside Chaucer, n. 3990 p. 850)
The narrator calls Symkyn a "market-betere," which is someone who loiters around a marketplace looking for a fight. (Source)
Symkyn is actually a diminutive (nickname) of the name Symond unique to East Anglia, where the story is set. (Source: Riverside Chaucer, n. 3941, p. 850).