Some of the missions had long, complicated names that were often shortened. For example, San Fernando Rey de Espana is usually referred to as ‘San Fernando Rey’ or’San Fernando.’ A couple missions have alternate names. San Francisco de Asis, is commonly called Mission Dolores (originally named after a stream that passed by). San Francisco Solano is also referred to as Mission Sonoma (for the town in which it is located).
I am not aware of any common abbreviation or shorthand reference for San Juan Bautista. It may be shortened to San Juan by some. There are, of course two missions with San Juan in their name, the other being San Juan Capistrano.
San Juan Bautista was called the Mission of Music by early historians.