Cllr Sam Locke had proposed that Abbey Court be named Abbey Court Christie Hennessy Place.
Council management said to rename an area would involve a plebiscite or a vote of those affected by the change.
Councillors decided that dedicating the area to Christie Hennessy instead would be a better course of action.
A plaque is also to be erected to mark the dedication.
A statue of the singer is already in the area.