In the letter to the third church, Jesus reminds them that when he speaks, it is the word of God. It is the final word. It breathed life into the world. It is the standard by which everything is judged. It can be trusted beyond all else.
He reminds them of these facts, because they live in a place that is very hostile to the family of God. He calls it the throne of Satan. He doesn't say why specifically. Certainly, because of its oppression. (One of the church's leaders was executed in a particularly nasty way.) But he does commend them for being faithful in the face of the oppression.
But he does warn them about an area they are failing in. They are allowing disrupting influences to remain in their midst. They are allowing a group of people who do not hold to God's standards to influence them. They have not broken away from the sins of the people. Scripture specifically mentions eating meat sacrificed to idols, and committing immorality. They are not honoring God with their lives.
NOTE: It occurs to me that these people may not have fully given their allegiance to Jesus. Part of worship of idols at that time was participating in feast honoring a particular God, and visiting the temple prostitutes. We have people with one foot in one camp, and one in the other. So, the influence God wishes his children to have in the city has been polluted.
The second group who are influencing God's family wrongly are identified as the Nicolaitans. There is no certain definition of how these people were polluting the family of God. Some hold that these were followers of an early disciple of Jesus, who chose to follow the Gnostic philosophy. (Which held that only the spiritual world was true. The physical world was more or less illusion, so it did not matter at all what one did in it.) Others held that these were people oppressors. Possibly leaders in the church who did not walk in the love and service that Jesus commanded leaders to follow.
Jesus simply commands the church to repent, or he will bring judgment on the church. He encourages them to persevere and choose obedience. If they persevere, he will first give them a special food. He uses the word "manna" which identifies the food God miraculously provided in the wilderness, sustaining Israel for 40 years.
And he will give them a new identity. The symbol was a white stone with a new name. Only the person receiving the stone will understand what the name means. There will be a new identity and a new relationship with God, special and unique for each person.