John 16:24 - Matthew Poole's English Annotations on the Holy Bible

All the prayers of believers under the Old Testament were accepted upon the account of the Mediator, who was typified by the temple, and the ark, where their solemn worship was performed by Divine appointment; but the explicit naming of him was not usual in their requests. Indeed the prophet Daniel enforced his requests for the Lord's sake, which may peculiarly respect the Messias, the promised Mediator. Our Saviour, in the form of prayer dictated to his disciples, gave no direction of addressing themselves to God in his name. But now he was ready to accomplish the will of his Father, by offering himself as an expiatory sacrifice for sin, and thereby reconciling God to them; and the prevalence of his intercession depending upon his meritorious, all sufficient sufferings, he directs and encourages them to pray with a humble confidence in his name for all the blessings they stand in need of. And it is matter of exceeding joy, that notwithstanding their unworthiness of the least favours, yet they are assured of obtaining their petitions offered up in his name; for the Father was so pleased with his voluntary obedience to the death of the cross, that no blessing is so good or great, but he most willingly bestows for his sake to all humble supplicants.