If you've already created a server notices user, say with the following config:

server_notices:
  system_mxid_localpart: 'notices'
  system_mxid_display_name: 'Server Notices'
  system_mxid_avatar_url: 'mxc://example.com/abcde12345'
  room_name: 'Server Notices'

change either system_mxid_display_name or system_mxid_avatar_url will not update the user's avatar or display name. These are only set on initial creation of the user, thus changing system_mxid_localpart will apply the changes, but in the process create a new user.

The code for setting the displayname and avatar is:

Instead, Synapse should check to see if the displayname or avatar has changed after a server restart, and update them accordingly.