I just wanted to add something in regards to this statement that I made:
There are other groups out there that believe as you said. They don't believe in the Trinity. They believe the Holy Spirit is another name for God or believe that the Holy Spirit is the power of God. I don't think these beliefs qualify to be called "Oneness".
I think, from what I have run into, that these groups also deny the Deity of Christ. At least "Oneness" believes in the Deity of Christ. They would have to since they believe Jesus is God the Father, Son and Holy Spirit and not three persons, but three different ways to manifest the one God.