Suffering was inevitable for Peter’s powerless Christian parishes. Peter has one clear point of view: any suffering ought to be the result of being a Christian. It is summed up in bearing the “name.”
Notice these two lines:
4:14: If you are reviled for the name of Christ, you are blessed, because the spirit of glory, which is the Spirit of God, is resting on you.
4:16: Yet if any of you suffers as a Christian, do not consider it a disgrace, but glorify God because you bear this name.
That “name” is Jesus Christ and they are being called “Christians”: devoted to Jesus, followers of Jesus, little Christs. The expression, which finds a potent parallel in Mark 9:41 (cf. Matt. 10:40-41): that is, they are suffering because they belong to Jesus Christ.
Inherent to the powerlessness of these communities was the potent combination of being both socially powerlessness and spiritual connection: they suffer because they are Christians and their social status puts them in a spot where they can do next to nothing about it.
To counter that Peter urges them over and over to be good, to be Christian, to follow Jesus.
And he grounds this once again in judgment:

For the time has come for judgment to begin with the household of God; if it begins with us, what will be the end for those who do not obey the gospel of God? 18 And
“If it is hard for the righteous to be saved,
what will become of the ungodly and the sinners?”
Therefore, let those suffering in accordance with God’s will entrust themselves to a faithful Creator, while continuing to do good.