Habitational name from any of the forty or so places in southwestern England called Beer(e) or Bear(e). Most of these derive their names from the West Saxon dative case, beara, of Old English bearu "grove, wood". Some may be from Old English bar "boar" or byre "hut, shed".
Beer 2
Type Surname (from given name, from occupation, from location & from nickname)
From Middle Low German bare, Middle Dutch bere "bear". Given as a nickname to someone who was thought to resemble a bear, a metonymic occupational name for someone who kept a performing bear, or a habitational name for someone who lived near a sign depicting a bear. Could also be a variant spelling of Bier.