Rebuilding a brand after a merger of two small companies

Two regional engineering consultancies merged last year and we still operate under both names. Clients are confused, our website is duplicated and proposals carry two logos. The partners are emotionally attached to their old brands.

We ran short interviews with clients, who mostly cared about continuity of their contact persons rather than the name. Our plan is a new master brand with a transition period of twelve months where the old names appear as "now part of". How did you handle brand consolidation after a merger without alienating loyal clients?