The apostolic interpretation of Jesus' words is demonstrated consistently in the biblical record. The name of the Lord Jesus Christ is the Name of the Godhead bodily. Notice that it pleased the Father that in Him (Jesus) should all fulness dwell.
The name of the Father, and the Son, and the Holy Spirit is expressed in Jesus. Also, Jesus is the family name Paul mentioned in Ephesians.(3:14-15) This truth is expressed by Paul over and over in scripture. (Col 2:12, Gal 3:27, Rom 6:3-4, 1 Cor 1:10-17) In addition, Paul reminds the Corinthians that they were not "baptized into the name of Paul" but into the name of the one who was crucified for them. Of course everyone knows who that was, it was none other than the Lord Jesus Christ.
"And he is the head of the body, the church: who is the beginning, the firstborn from the dead; that in all things he might have the preeminence.
For it pleased the Father that in him should all fulness dwell;..." (Col 1:18-19)
"In Him (Jesus) dwells all the fullness of the Godhead (Father, Son and Holy Ghost) bodily." (Col 2:9)
"For this cause, I bow my knees unto the Father of our Lord Jesus Christ,
Of whom the whole family in heaven and earth is named," (Eph 3:14-15)