Rev 3:7-13

THE SPIRIT TO PHILADELPHIA
7 “To the angel of the assembly in Philadelphia write: “He who is holy, he who is true, he who has the key of David, he who opens and no one can shut, and that shuts and no one opens, says these things: 8 “I know your works (behold, I have set before you an open door, which no one can shut), that you have a little power, and kept my word, and didn’t deny my name. 
Rev 3:7
have kept My word – from John 14:23 – “If anyone loves Me, he will keep My word…and We will make our abode with him.” Hence, Jesus here says, “I have put before you an open door which no one can shut.”
9 Behold, I give of the synagogue of Satan, of those who say they are Jews, and they are not, but lie. Behold, I will make them to come and worship before your feet, and to know that I have loved you. 
Rev 3:9
the synagogue of Satan – see comments under Rev 2:9
10 Because you kept the word of my patience, I also will keep you from the hour of testing, that which is to come on the whole world, to test those who dwell on the earth.
Rev 3:10
the hour of testing – the coming of the Antichrist, see 1 John 2:18. “the Antichrist is coming . . . this is the last hour.”
11 I come quickly. Hold firmly that which you have, so that no one takes your crown. 12 He who overcomes, I will make him a pillar in the temple of my God, and he will go out from there no more. I will write on him the name of my God, and the name of the city of my God, the new Jerusalem, which comes down out of heaven from my God, and my own new name. 13 He who has an ear, let him hear what the Spirit says to the assemblies.
Rev 3:12
My God – is repeated three times in this verse. While the Spirit of Christ and the Father “are one” in the LORD’s Day, the Father is always the one true God.

I will write on Him the name of My God – the name of Jesus, which is also the name of the “the City of My God, the New Jerusalem.” The body of Christ, the Church of God, must bear His name: “God saves.”   That Christ, Jerusalem, and the righteous, bear the name of God is the understanding of rabbinic theology from at least the 1st Century BC. From the Talmud, we read: “Said R. Samuel Bar Nahmani said R. Yohanan, ‘There are three who are called by the name of the Holy one, blessed be he, and these are they: the righteous, the Messiah and Jerusalem.’”1Christ was prophesied to share the name of Jerusalem in the Book of Jeremiah, compare Jer 23:6; and Jer 33:16, where the name is “the Lord is our righteousness.”

My new name – after Christ endured the cross, God gave Him “the name above every name,” (Phil 2:9). This is the glory and reputation that the saints will share if they also overcome; see John 17:22.