You are absolutely correct! However, I think there is much more involved. His will and authority are worthless apart from His provision to make approach to God possible. Hebrews 10:10-22 demonstrates that the possibility of coming before the presence of the Father is completely based upon the provision of Christ as both sacrifice and High Preist together forming the mediation between God and man. To come before the Father "in the name of Jesus" is to believe and confess that Jesus is the basis for approaching God. That is, He is the complete satisfaction of God's wrath and righteousness in regard to the petitioner. To pray "in the name of Jesus" is to embrace the very essence of the gospel as the personal basis to approach God for anything including prayer:
19 ¶ Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus,
20 By a new and living way, which he hath consecrated for us, through the veil, that is to say, his flesh;
21 And having an high priest over the house of God;
22 Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water.
To pray "in the name of Jesus" is to come before God and petition of the Father through mediation of the Christ provision. It is to come to the Father not on your merits but his merits, not by your righteousness but by his righteousness, not by your faithfulness but by his faithfulness, not by your authority but by his authority, not according to your will but according to His will. It is to come through both the sacrifice and mediatorial Priesthood of Jesus Christ as a completed, satisfactory, sufficient, substitutionary provision.