Holy means set apart by God for a purpose. Christians are "holy". We are set apart by God for a purpose.
The term "holy spirit" is an english description of a force that is emanating from God. It can be felt and it has an impact but we are unable to comprehend it fully because as humans we are incapable of comprehending "spirit"...whatever it is.
Since there is not a way to comprehend God...who is made of "spirit"....a term is used to explain this influence. The term used in greek for spirit is "pneuma" which literally means a wind, breathe or breeze. In other words something that can be felt and that can have an effect on things but yet can't be seen.
This set aside spirit has a purpose. In this case it's a bit of God that resides in Christians. A portion of his spirit. It's purpose, the purpose of God, is to change and transform us...to make us grow in love...God's character...which leads to faith and hope.
Where we differ is that I believe that the holy spirit is NOT another being in Godhead of three. When the term holy spirit is used it is the influence of NONE other then God in our lives. Correct me if I'm wrong but you think there is a separate being other then the father and son, a being called "the holy spirit". Is that correct?
The Universe God has created has realms we are not fashioned to sense, in our present body, soul, spirit configuration. These realms exist and are real. Here, I should give you two axioms which benefit my reasoning:
Without Time, events do not occurWithout Space, things do not exist
These axioms are important for anything in the created Universe. God is greater than His creation, BUT He has chosen to also be in His creation, as The Holy Spirit and as Jesus. The dimensional complexity/simplicity of some realms beyond our sensing is not a barrier to God in His creation You will recall Jesus leaving the burial tomb without rolling away the stone and appearing in a locked and shuttered room without opening a window or door. There is also a scene in Daniel chapter 5 where a being not in the same realm as Palace party central reaches into the spacetime of the Babylonian king, to write upon the wall; just the hand is seen, but there was a being with spatial and temporal reality to which the hand was attached ... the being was in the Created Universe but the realm in which the being exists was not sensed by the partiers except where the being intersected the spacetime of the Palace room.
Now to answer your question. God IS greater than His creation, but The Father Almighty has aspects (named Jesus and The Holy Spirit) which/Who interact with the created Universe. These interactions do not diminish God but we sense them as two 'other' personas of The One God, the aspects where The Creator Almighty interacts with His Creation. As a Christian I am saved by the work of one aspect of God (His Holy Spirit interacting with my human spirit) BECAUSE of the work another aspect of the One God (Jesus) has performed on my behalf.
Conversation is enhanced by using the term 'person of' when referring to one or another of the Three Known aspects of The One God. But each does not diminish the Father Almighty as He is omnipotent, omnipresent, and greater than His Created Universe in which we and perhaps a huge variation of living beings exist in realms we were not fashioned to be able to sense.
That said, there is coming soon a moment of transformation, when the corruptible will put on incorruption, the mortal put on immortality, and we shall gather in the clouds to meet the Lord in the air while seven years of God progressively pouring out His wrath upon the Earth which rejected His Grace in Christ. ... BTW, the Universe we sense is so delicately balanced that a change in one parameter or another to a fraction of 1/10120 would end out living spacetime environment! Such a small change would make life as we know it impossible.