Is there a list of all the nicknames used for each mission.

Here is a list of mission abbreviations in common use and the special 'designations' that Fr. Zephyrin Engelhardt, O.F.M. cited in his definitive multi-volume study The Missions and Missionaries of California, and smaller books on specific missions:
San Diego de Alcala San Diego Mission Mother of the Missions
San Carlos Borromeo de Carmelo Mission Carmel  
San Antonio de Padua San Antonio Mission  
San Gabriel Arcangel San Gabriel Mission Pride of the Missions
San Luis Obispo de Tolosa Mission San Luis Obispo  
San Francisco de Asis Mission Dolores  
San Juan Capistrano San Juan Capistrano Jewel of the Missions
Santa Clara de Asis Mission Santa Clara  
San Buenaventura San Buenaventura Mission by the Sea
Santa Barbara Santa Barbara Queen of the Missions
La Purisima Concepcion La Purisima  
Santa Cruz Mission Santa Cruz  
Nuestra Senora de la Soledad Mission Soledad  
San Jose San Jose  
San Juan Bautista San Juan Bautista Mission of Music
San Miguel Arcangel San Miguel Mission  
San Fernando Rey de Espana San Fernando Rey Mission Mission of the Valley
San Luis Rey de Francia San Luis Rey Mission King of the Missions
Santa Ines Virgen y Martir Mission Santa Ines Mission of the Passes
San Rafael Arcangel San Rafael Mission  
San Francisco Solano Mission Sonoma