Graphs with the same name must be assigned to different members. A signle member cannot have a two graphs with the same name.
If you are trying to assign a graph to a team member who has not been invited to your organization, the graph will not save.
If you have several organizations listed in your account, check that the team member you are trying to assign the graph to is a member of that organization.
Add the user to the organization via settings, or
Change the organization of the graph to the one that the member is in.