Isaiah 63:11 Then he remembered the days of old, Moses, and his people, saying, Where is he that brought them up out of the sea with the shepherd of his flock? where is he that put his holy Spirit within him?
In Isaiah 63:11, the word "Spirit" is the Hebrew word rū-aḥ. The first use of the word rū-aḥ is Gen 1:2 which states and the Spirit of God moved upon the face of the waters.
We know from Eph 4:4 that there is one Spirit. So we know that the Holy Spirit before Pentecost is the same Holy Spirit after Pentecost. And we know from John 14:26 that the Comforter is the Holy Spirit.
While I believe the Holy Spirit of the OT is the same Holy Spirit of the NT, I also believe that in OT, the Spirit rested upon God's people and in our day and time the Holy Spirit dwells within those who are born again.