Regarding the Holy Spirit, there is only one Spirit of God,
so there is only one Person(as Deity)
of the Spirit, at the same time the Spirit of the Son and of the Father that is the Holy Spirit. To reiterate again, the Holy Spirit is the Spirit of God in action, it is
now the Spirit of Christ in action…(see John 14: 18,
Revelation 2:7, Acts 9:4-5 and 2 Corinthians 3:17)
The Holy Spirit is one of the three Persons of the Triune God.
His distinct Personhood is shown by the fact that Jesus called him "another Comforter" or helper (Parakletos) that Jesus would send (again, this word conveys personal interaction). This Person is not Jesus, who is a Comforter as well. See 1 John
John 14:16 And I will pray the Father, and he shall give you another Comforter, that he may be with you for ever,
1 John 2:1 My little children, I am writing these things to you so that you may not sin. But if anyone does sin, we have an advocate with the Father, Jesus Christ the righteous (ESV Strong's)
The word "Comforter" and "advocate" are the same in Greek (parakletos).
In one sense, you could call the Holy Spirit the "Spirit of Christ" or "Spirit of the Father" because there is only one God, and the three Persons mutually indwell one another. This is part of what "one God" means. There is a mutual indwelling.
John 14:11 Believe me that I am in the Father and the Father is in me, or else believe on account of the works themselves.
John 14:10 Do you not believe that I am in the Father and the Father is in me? The words that I say to you I do not speak on my own authority, but the Father who dwells in me does his works.
And, I will be quite honest with you..in the USA Oneness Pentecostals are considered to be some of the most ignorant people within professing Christiandom. Their "scholars" are generally from places with lower levels of education like the deep South. I am not claiming all people from the deep South are ignorant, but there is a tendency towards this. As I watch debate videos with Oneness Pentecostals and apologists like James White, I am not impressed with them.
There is one redeeming virtue about them, though. Most believe the Bible is the truth, even though they've been indoctrinated into a false interpretation of it. This is similar to me as a cultist. I was a dumb twenty-something when I began studying the Bible and believing their false, anti-Trinitarian rhetoric, but at least I believed the Bible was the word of God. That's a starting place. All you need to do is get past their ignorant, false, conspiracy-level view of Christianity and then you might make some progress