45 οἰκονομία 1.b renders the term here as “divine office.”
46 See πληρόω 3. The idea here seems to be that the apostle wants to “complete the word of God” in that he wants to preach it to every person in the known world (cf. Rom 15:19). See P. T. O’Brien, Colossians, Philemon (), .

In other versions

of which I became a minister according to the stewardship from God that was given to me for you, to make the word of God fully known,

I have become its servant by the commission God gave me to present to you the word of God in its fullness—

I have become its servant, according to God’s commission that was given to me for you, to make the word of God fully known,

God has given me the responsibility of serving his church by proclaiming his entire message to you.

of which I became a minister, according to God’s stewardship which was given to me for you, to complete the word of God,

Whereof I am made a minister, according to the dispensation of God which is given to me for you, to fulfil the word of God;

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