The short answer is “Absolutely”. But He has many names and titles because He has many different ministries. He is introduced to us right at the beginning of the Bible as “the Spirit of God”. And He is found throughout the Bible from Genesis to Revelation. So why does everyone not simply believe that He is God the Holy Spirit? Two reasons (a) Satanic deception and (b) willful blindness.
In the Bible He is called “the Spirit”, “the Holy Spirit”, “the Spirit of God”, “the Spirit of Holiness”, “the Spirit of Truth”, ”the Comforter”, or “the Paraclete”, as well as “the Holy Ghost”.
How did He come to be called “the Holy Ghost”? It would appear that since Martin Luther’s German translation came into existence long before the King James Bible, it did have an influence on the English translation. The German equivalent for “spirit” is “geist” which translates into “ghost”. So it is perfectly accurate to call the Holy Spirit “the Holy Ghost”. Unfortunately the KJV translators failed to consistently capitalize “Holy Spirit” or “Spirit” (where applicable). When it is God the Holy Spirit, it is necessary to capitalize those words, so that there is no misunderstanding.
But how do we know that He is God? Because He has all the attributes of God according to Scripture. Indeed He is the Author of Scripture (2 Timothy 3:16,17; 2 Peter 1:19-21)
Is He a Person who can be vexed? But they rebelled, and vexed his Holy Spirit: therefore he was turned to be their enemy, and he fought against them. (Isa 63:10)
Is He a Person who can be lied to? But Peter said, Ananias, why hath Satan filled thine heart to lie to the Holy Ghost, and to keep back part of the price of the land?
Is He a Person who can be grieved? And grieve not the Holy Spirit of God, whereby ye are sealed unto the day of redemption.(Eph 4:30)
Is He a Person who can lead another person? And Jesus being full of the Holy Ghost returned from Jordan, and was led by the Spirit into the wilderness (Luke 4:1)
Is He a Person who can cause men to speak foreign languages supernaturally? And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance (Acts 2:4)
Is He a Person who can reveal spiritual truths to men? Which in other ages was not made known unto the sons of men, as it is now revealed unto his holy apostles and prophets by the Spirit (Eph 3:5)
One could write a dissertation on the Holy Spirit, but this is more than enough to establish the truth about God the Holy Spirit.
“And we know that
the Son of God is come, and hath given us an understanding, that we may know him that is true, and we are in him that is true, even in his Son Jesus Christ. This is the true God, and eternal life.”
1 John 5:20 KJV
The spirit of Jesus Christ is one
“searching what, or what manner of time
the Spirit of Christ which was in them ( the old testsment prophets ) did signify, when it testified beforehand the sufferings of Christ, and the glory that should follow.”
1 Peter 1:11 KJV
The holy spirit is not independent from the father and son it is the spirit of Jesus manifest in the gospel
“But ye are not in the flesh, but
in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not
the Spirit of Christ, he is none of his. And if Christ be in you, the body is dead because of sin; but
the Spirit is life because of righteousness.”
Romans 8:9-10 KJV
The spirit of God is the holt spirit , the spirit of Christ the spirit of Gods son
“And because ye are sons,
God hath sent forth the Spirit of his Son into your hearts, crying, Abba, Father.”
Galatians 4:6 KJV
The holy spirit is Gods spirit its the spirit of Christ the same spirit in believers
“Know ye not that ye are the temple of God, and that the Spirit of God dwelleth in you?”
1 Corinthians 3:16 KJV
there’s just one spirit because there’s just one God and it’s his spirit shared with believers
“There is one body, and one Spirit, even as ye are called in one hope of your calling; one Lord, one faith, one baptism, one God and Father of all, who is above all, and through all, and in you all.”
Ephesians 4:4-6
the holy spirit , Jesus the son and God th father aren’t independent of one another the father is in heaven the sin came to earth and the spirit is in the hearts of believers
It’s how God is filling creation by giving us his living spirit the same spirit that feels in Christ the man who is the spirit
“
Now the Lord is that Spirit: and where the Spirit of the Lord is, there is liberty.”
2 Corinthians 3:17
“
God is a Spirit: and they that worship him must worship him in spirit and in truth.”
John 4:24 KJV
https:
in your eye. 
