What would be the correct one? Father, son and Holy Spirit or only Jesus? I feel like I may have to be rebaptized? Yes, the baptism into the Holy Spirit would be in Jesus' name, but keep in mind everyone who had received that baptism had received the baptism of repentance before (Acts 1:5 and as well as Acts 9). Allow me to be confused.
Christian Baptism is "in the name of the Father, Son, and Holy Spirit" as per Christ's command in Matthew 28:19.
When we see "baptized in the name of Jesus" or similar language in the Acts of the Apostles, it may be helpful to understand this as "by the authority of Jesus", it marks a distinction between Christian Baptism which Christ instituted for His Church and other "baptisms", such as John's baptism of repentance, or the "baptisms" associated with Jewish ritual purification.
Historically and traditionally the method of Baptism is less important than the form. Method meaning, for example, whether one is immersed three times (the most ancient method of Christian Baptism), immersed a single time, or whether it is by diffusion (pouring), or aspersion (sprinkling). All of these methods have been generally accepted as valid throughout the history of Christianity, and the earliest Christian witness to the method(s) of baptism (the Didache, written sometime between 60 and 120 AD) mentions that immersion in running water is preferable, but still water is acceptable, and if there just isn't enough water to immerse, pouring is fine. The method is not what matters, but rather the form.
And the form of baptism is that there is the application of water in which one is baptized "in the name of the Father, Son, and Holy Spirit". Not because the words are somehow magic, but rather to properly communicate what is happening. The general reason why Christians have rejected "Jesus name only" formulas is because these are associated most often with sectarian groups whose baptisms are illicit and invalid because they are intentionally contrary to the Christiant intent and meaning of baptism. So, for example, in modern times "Jesus' name" baptism is most commonly associated with "Oneness Pentecostals", who flagrantly deny the Trinity, and who baptize not into Christ, but rather baptize into their own sect. And thus their baptisms are considered invalid. In the same way, Mormon baptisms are considered invalid, even though they do baptize "in the name of the Father, Son, and the Holy Spirit"--it's not the words themselves, but the meaning and intent.
As such the majority of Christians, from across different traditions and communions, all recognize baptisms as valid regardless of who officiated it, or where it was done, as long as it is a valid Christian baptism. That means, for example, Catholics, Lutherans, Anglicans, Prebyterians, etc, completely acknowledge one another's baptisms, and acknowledge baptisms in Baptist, Pentecostal (Trinitarian), non-denominational, etc churches; even if Baptist, Pnetecostal, non-denominational churches may not recognize Catholic, Lutheran, Anglican, etc baptisms as valid.
Because the historic understanding is that baptism is not about joining a congregation, or making a public confession of faith, but is instead a means of grace through which God Himself works, to create, give, and strengthen faith. So as long as one is baptized as a Christian, it is a Christian Baptism.
In the name of the Father, Son, and the Holy Spirit, for here God stakes His own Name in His Sacrament, sealing us with His word and promise which He gives us in Christ, and so here the Father, the Son, and the Holy Spirit are found. For we are adopted as children of the Father, united to Christ's death and resurrection, and have the promise of the Holy Spirit--all which are promised and declared in Holy Scripture as true.
-CryptoLutheran
Do we have any NT support for seeing it as the OT concept of admission into the earthly people of God?