The group said the Morrison name would only be used for non-PFI projects in Scotland and for tenders with rival utility groups.
Chris Mellor, AWG's chief executive, said: "The Morrison brand is very valuable, notably in a Scottish context and where branding is a sensitive issue for some water companies. But with these exceptions, the plan is to move to the AWG brand."
AWG said the move would be completed over the next 18 months. The group used the name AWG Project Investments to bid for a £90m public–private partnership with the Defence Housing Executive.
Nigel Hawkins, utilities analyst at Williams de Broë, said: "I am not surprised AWG is making this move given what the company is setting out to do, which is to provide infrastructure services to other utilities. While the Morrison brand has value in the construction sector, it has less clout in the utilities sector."
AWG has recently been split into two operating companies. The first consists of its water interests and the second groups its five construction and civil engineering divisions (utilities, construction, facilities management, rail and PFI).
Morrison Construction presently makes up 27% of the group's £1.2bn turnover. Of the contractor's six regional businesses, the five outside Scotland will move to the AWG brand.
While the Morrison brand has value in the construction sector, it has less clout in the utilities sector
Nigel Hawkins, utilities analyst
Details of how the changeover is to be implemented are yet to be agreed.
Anglian Water, as AWG was previously known, shocked the City in August 2000 when it bought builder Morrison for £265m.
The deal was part of AWG's medium-term strategy of moving from supplying water to supplying infrastructure to other utilities.
The group wrote off £22m from Morrison's value after discovering that six contracts it had taken over would not be worth as much as first thought.
Five of the contracts have since been resolved. The final contract is due for completion.