I think your reply raises the point that there may not be one solution. It greatly depends on context and reasons/objectives associated with this new identity.

My experience shows that in an environment with a very stable and well established brand a logo and project identity made sense because we were implementing a far-reaching change of major strategic importance to the business.

In other contexts, it will be more important to fit into the “one company image or branding” mindset.

Above all, I think this highlights the need for the consultant to be in tune with a companies communication environment and the strategy being followed by the Director of Communications.

This is quite a challenge in most organizations. In India, as part of the internal communications team, I am bombarded with requests for new logos and colors to differentiate projects and campaigns. It takes a great deal of effort to push back with a rationale on why a consistent ‘one company image or branding’ is vital. I am aware that Accenture ( where I worked in my previous assignment) disallows coining new names or creating icons to promote internal teams and projects. At best, the team name in plain text is allowed. Even that is run past the global brand team and naming experts.
I guess it is dependent on how each organization views its branding. Some are casual ( encouraging employee creativity), while others believe quite strongly in the opposite.

I personally believe that promoting a new program or launching a new team requires focus on the key messages and internal branding nomenclature. Confusing names and icons can clash with the overall internal branding effort.