this is my prayer (the sequel)

Ephesians 3:14-21

Paul's request for the Ephesian church: that they would be strengthened with power, that Christ may dwell in their hearts, that they would have the capacity to understand the dimensions of Christ's love and experience that love, that they would be filled to all the fullness of the measure of God.
There are a couple of phrases that I have questions about: First, what does it mean that every family in heaven and on earth derives its name from the Father? Second, is the meaning of being filled with all the fullness of the measure of God really what it seems to mean?
I don't think that Paul is praying that the individual Christian would be filled with the fullness of God. This is a corporate letter written to a church body so I think that it's the church body that gets filled in this way. This also fits better with the tone of the rest of the letter: the church is the fullnes of him who fills all things in all ways (1:23) and the church unified shows the wisdom of God to the rulers of the spiritual realm (3:10).
I also have confidence that this prayer will be answered based on Paul's next statement: God can do more than we can ask or imagine for his glory. Christ brought glory to God and now, according to this prayer and other passages of Scripture, the Church's role is to bring glory to God. In the context of this letter, we do that when we are unified.