Yea, so have I strived to preach the gospel, not where Christ was named, lest I should build upon another man's foundation:

People's New Testament

15:20 Yea, so have I strived to preach. He declares the fixed policy of his ministry not to preach where Christ had been heard, but in new fields. Where other apostles or evangelists had laid a foundation, he did not seek to build. Compare 2Co 10:12-16. As no apostle or great evangelist had yet visited Rome, his letter to the Romans was no violation of his principle.

Wesley's Notes

15:20 Not where Christ had been named - These places he generally declined, though not altogether, having an holy ambition (so the Greek word means) to make the first proclamation of the gospel in places where it was quite unheard of, in spite of all the difficulty and dangers that attended it. Lest I should only build upon another man's foundation - The providence of God seemed in a special manner, generally, to prevent this, though not entirely, lest the enemies of the apostle, who sought every occasion to set light by him, should have had room to say that he was behind other apostles, not being sufficient for planting of churches himself, but only for preaching where others had been already; or that he declined the more difficult part of the ministry

Jamieson-Fausset-Brown Bible Commentary

20, 21. Yea, &c.-rather, "Yet making it my study (compare 2Co 5:9; 1Th 4:11, Greek) so to preach the Gospel, not where Christ was [already] named, that I might not build upon another man's foundation: but (might act) as it is written, To whom no tidings of Him came, they shall see," &c.

Matthew Henry's Concise Commentary

15:14-21 The apostle was persuaded that the Roman Christians were filled with a kind and affectionate spirit, as well as with knowledge. He had written to remind them of their duties and their dangers, because God had appointed him the minister of Christ to the Gentiles. Paul preached to them; but what made them sacrifices to God, was, their sanctification; not his work, but the work of the Holy Ghost: unholy things can never be pleasing to the holy God. The conversion of souls pertains unto God; therefore it is the matter of Paul's glorying, not the things of the flesh. But though a great preacher, he could not make one soul obedient, further than the Spirit of God accompanied his labours. He principally sought the good of those that sat in darkness. Whatever good we do, it is Christ who does it by us.