If agreed, the new name will be the Association of Local Government Communicators or LGcommunicators.
The recommendation has been circulated to all member councils inviting their support - including some new district councils members. The identity includes a new strapline: 'The national voice for communications in local government.'
The move follows the recent revised publicity code recognising the community leadership role for councils contained in the Local Government Act 2000.
Local authorities are now required to consult more widely and allow local people to have an informed say about the issues that affect them.
Society chair Julie Hollings, head of communications at Isle of Wight Council, said: 'We have been working on developing a new identity and name for the society to reflect our new responsibilities.'