Zarza is very common in minor toponymy and alludes to the rosaceous plant thus named, probably with a collective meaning applicable to the wild, scrubby terrain, which is still present in Portuguese; the toponyms Zarza are equivalent to ‘bush’ or ‘rockrose’. La Mayor is distinguished from the others by the importance of the town, which was the head of an encomienda. See Castaño Fernández (382-384).

Cited bibliography: 

Castaño Fernández, Antonio M. Los nombres de Extremadura. Estudios de toponimia extremeña. Mérida: Editora Regional de Extremadura, 2004.