You were able to update a group using the REST API without the name on RH-SSO 7.4.x, however on 7.6.x that isn't possible, since the same become mandatory, according to the code [1]:

/**
     * Update group, ignores subgroups.
     *
     * @param rep
     */
    @PUT
    @Consumes(MediaType.APPLICATION_JSON)
    public Response updateGroup(GroupRepresentation rep) {
        this.auth.groups().requireManage(group);

        String groupName = rep.getName();
        if (ObjectUtil.isBlank(groupName))

{             return ErrorResponse.error("Group name is missing", Response.Status.BAD_REQUEST);         }

        if (!Objects.equals(groupName, group.getName())) {
            boolean exists = siblings().filter(s -> !Objects.equals(s.getId(), group.getId()))
                    .anyMatch(s -> Objects.equals(s.getName(), groupName));
            if (exists)

{                 return ErrorResponse.exists("Sibling group named '" + groupName + "' already exists.");             }

        }
        
        updateGroup(rep, group)

adminEvent.operation(OperationType.UPDATE).resourcePath(session.getContext().getUri()).representation(rep).success();
        
        return Response.noContent().build();
    }

 

But, the API Documentation still saying that "name" is optional [2]

 

[1] https://github.com/keycloak/keycloak/blob/ef47eee2dda29a0f08187ae67970323c28947f11/services/src/main/java/org/keycloak/services/resources/admin/GroupResource.java#L99

[2]https://access.redhat.com/webassets/avalon/d/red-hat-single-sign-on/version-7.6/rest-api/#_grouprepresentation