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The name of the move group is /move_group.
Alternatively to the /move_group action, one can generate a trajectory path using the plan_kinematics_path, and the /plan_sequence_path services.
Trajectory Execution
Moreover, MoveIt provides the /execute_trajectory action to execute ROS trajectory messages. If you need a good example on how to use the MoveIt without using the MoveIt libraries, you can take a look at the moveit_python implementation: https://github.com/mikeferguson/moveit_python/blob/ros1/src/moveit_python/move_group_interface.py
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