Although as Dottard's answer shows that ultimately the savior is God the Father (whose proper name is the Tetragrammaton) acting through His Son incarnate Jesus of Nazareth, and although Peter himself in his Acts 2:14-47 sermon quoted Joel 2:28-32 which DOES refer to the Tetragrammaton:
And it shall be that everyone who calls on the name of the Lᴏʀᴅ will be saved.’
the context of Acts 4:12 should make the answer obvious that what Peter meant by "the name", is the name of His Son: Jesus of Nazareth.
The enclosing passage is the pericope Acts 4:1-22 where there are many references to "the name" such as:
When they had placed them in the center, they began to inquire, “By what power, or in what name, have you done this?” Then Peter, filled with the Holy Spirit, said to them, “Rulers and elders of the people, if we are on trial today for a benefit done to a sick man, as to how this man has been made well, let it be known to all of you and to all the people of Israel, that by the name of Jesus Christ the Nazarene, whom you crucified, whom God raised from the dead—by this name this man stands here before you in good health.
... But so that it will not spread any further among the people, let’s warn them not to speak any longer to any person in this name.” 18 And when they had summoned them, they commanded them not to speak or teach at all in the name of Jesus.
NLT translation makes it a little more obvious by translating Acts 4:12 this way, adding the implied subject of the sentence (God the Father):
There is salvation in no one else! God has given no other name under heaven by which we must be saved.”
Furthermore, Jesus Himself gave permission to the apostles in John 4:13-14 to ask in His name in the pericope discussing His relationship to the Father (John 4:1-14). It's obvious from the context that Jesus did NOT teach the apostles to ask in YHWH's name.
For a scholarly reference, here's a confirmation from a commentary: A Critical and Exegetical Commentary on the Acts of the Apostles, Volume 1:
ἐν ἄλλῳ οὐδενί, in no other person. It would be possible to supply ὀνόματι, which would suit the preceding verses, but the clause that follows, introduced by γάρ, deals with the name, and the logic of the argument runs: In no other person is there salvation, because there is no other name than that of Jesus by which … There is a close verbal parallel in Josephus, Ant. 3:23: ἐν αὐτῷ γὰρ εἶναι τὴν σωτηρίαν αὐτοῦ καὶ οὐκ ἐν ἄλλῳ. This suggests that there is little point in an attempt to distinguish between ἄλλος and ἕτερος. There is a parallel in a different setting in Aristophanes, Lysistrata 29f., ὅλης τῆς Ἑλλάδος ἐν ταῖς γυναιξίν ἐστιν ἡ σωτηρία, and another in Herodotus 8:118:3, ἐν ὑμῖν γὰρ οἶκε εἶναι ἐμοὶ ἡ σωτηρίη.