Revelation 3:1 shows us that the church at Sardis had a name (G3586) that was undependable. At times they were ready to represent Jesus, but at other times it was as though they hadn’t even known him. Jesus claimed, however, there were a few names (G3586) in Sardis who had not soiled their garments (Revelation 3:4). That is, these names were ready both in season and out of season to reprove, to rebuke and to exhort with patience and instruction (cf. 2Timothy 4:2). They proved themselves that they were not ashamed of the name of Christ.
Jesus also said that these faithful believers would walk with him in white, because they were worthy. To be clothed in white is to come under the blood of Jesus (Revelation 7:13-14). To be clothed in white is to have put on Christ (Romans 13:4; Galatians 3:27), and to have put on a robe of righteousness (cf. Job 29:14; Isaiah 61:10).
These few names, who had not soiled their garments, would walk with Christ, because they were worthy (G514). The same Greek word is found in 2Thessalonians 1:3 where Paul was bound to thank God for the believers there, because they were worthy (G514), in that their faith grew above expectations, and they loved one another so much. Paul went on to say that he boasted to other churches of their faith, which continued to grow throughout all their troubles and persecutions (2Thessalonians 2:4), and Jesus seems to boast of the few faithful ones in Sardis, to move the unfaithful to repent. Paul concluded in 2Thessalonians 1:5 that the fact that they continued to grow in faith throughout their persecutions was “a manifest token of the righteous judgment of God” that they should be counted worthy “of the Kingdom of God, for which they all suffered”.
It seems that enduring trouble and persecution was necessary to be counted worthy of admittance into the Kingdom of God (2Thessalonians 1:5; cf. 2Timothy 3:12). Therefore, if such a thing is true, then these in Revelation 3:4 who were counted worthy by Jesus must have endured persecution for his name sake. If this is also so, then it may mean the majority of the church at Sardis sought to avoid persecution, even to the point of shunning the name of Christ in the presence of their enemies (cf. Mark 8:38). So, Jesus’ rebuking them was an effort to bring them to repentance, so that he could receive them.
Jesus went on to say that they who overcome would be clothed in white and would not have their names blotted out of the book of life. Instead, he would confess their names before his Father and his angels (Revelation 3:5). I believe the context in which the word overcome (G3528) is used in Revelation 3:5 concerns the believers’ faith in Jesus. They in Sardis are able to overcome the world only by trusting Jesus:
For whatsoever is born of God overcomes the world: and this is the victory that overcomes the world, even our faith. (5) Who is he that overcomes the world, but he that believes that Jesus is the Son of God (1 John 5:4-5)?
Jesus’ disciples are able to overcome the false teachers, who try to bring them under a different authority, because greater is he who is in the believers at Sardis than they who are in the world and speak against the name of Jesus (1John 4:3-6).
Moreover, Jesus told his disciples at Sardis that their names were written in heaven (Luke 10:20), and this understanding was also held and preached by Paul in the New Testament (Philippians 4:3). It was also understood in the Old Testament, and it appears that one’s name could be removed (Exodus 32:32). Although the book may not be literal, it does show that believer’s names are known and remembered in heaven. The Lord knows and remembers the names of his faithful disciples.
Having one’s name confessed before God and the angels has to do with whether or not one preached the Gospel to others, i.e. whether or not one was ashamed of Jesus and his words (Matthew 10:32: Mark 9:38; Luke 8:26; 12:8). Therefore, Jesus confession to his Father and the angels is probably in the same sense that Paul boasted of the church in Thessalonica to other churches he wrote to (2Thessalonians 2:4).
Finally, in Revelation 3:6 Jesus was speaking to those who had their names written in the book of life, namely, those who are known by God at Sardis, and he commands them to read what he says to all the churches, because they have ears that hear. In other words they have the Spirit of God who gives them understanding of spiritual matters.
 This in itself is proof that Sardis was never a dead church, as some wish to interpret Revelation 3:1.