By default the access log name is not case sensitive when trying to create a new access log. The following example shows that the access log name is not case sensitive when trying to create a new access log through the CLI:
#(config access-log)create log MAPI
% Log name already exists but with different case
#(config access-log)edit log MAPI
% Log does not exist.
#(config access-log)edit log mapi
#(config log mapi)
Moreover, the access logs are also case-sensitive when trying to edit the access log.
One of the reasons for this behavior (when creating new access log) is to prevent from the proxy admin from creating duplicate access log names that might cause issues when logging user access.