Although we're commanded to pray in Jesus' name, are we commanded to always say "in Jesus' name" in all our prayers?
It is possible to do something in Jesus' name without uttering the phrase "in Jesus' name". We're told to do all things in Jesus' name (Col 3:17), not just pray. Yet when we sing, we don't start off each song (or end each one) with the phrase "in Jesus' name". When we assemble, we don't announce that "we're meeting today in Jesus' name". This is because the unstated assumption is that when we meet as Christians (or change an old lady's flat tire, or walk past the brothel instead of into it, or give back the extra change the cashier incorrectly gave to us, etc), we're doing so in Jesus' name. There is no reason to announce this fact each time we do something (although there's nothing wrong with announcing it). Adding the phrase to each prayer is a man-made tradition that has become a doctrine for some of us.
Here are examples of New Testament prayers which do not include the phrase "in Jesus' name":
The Lord's Prayer : Matt 6:9-13; Luke 11:2-4
Jesus' Prayer for Unity : John 17
Jesus' prayer on cross, asking forgiveness for his murderers : Lk 23:34
Jesus' prayer on cross, asking "why" : Matt 27:46; Mark 15:34
Jesus' prayer on cross, committing his spirit to God : Luke 23:46
The prayer of the justified sinner : Luke 18:13-14
Prayer for Judas' replacement : Acts 1:24
Prayer of thanksgiving for God's help against the authorities : Acts 4:24ff
Prayer for unity among the Romans : Rom 15:5-6
Prayer for joy & peace in the Romans : Rom 15:13
Paul's closing prayer for the Corinthians: 2 Cor 13:13
Paul's prayer for the Ephesians : Eph 3:14-21
Paul's prayer for the Thessalonians : 1 Thess 3:11-13
Another of Paul's prayers for the Thessalonians : 1 Thess 5:23-24
Another of Paul's prayers for the Thessalonians : 2 Thess 2:16-17
Another of Paul's prayers for the Thessalonians : 2 Thess 3:16
Peter's prayer for the people of the Dispersion : 1 Pet 5:10-11
John's prayer : Rev 1:5b-6
John's prayer to Jesus for him to come : Rev 22:20
John's prayer for the grace of Jesus to be with all the saints : Rev 22:21
It is quite appropriate, however, to announce that what you're doing (or what God is doing) is being done through Jesus:
Rom 16:25-27: "25 Now to Him who has power to strengthen you according to my gospel and the proclamation of Jesus Christ, according to the revelation of the sacred secret kept silent for long ages, 26 but now revealed and made known through the prophetic Scriptures, according to the command of the eternal God, to advance the obedience of faith among all nations— 27 to the only wise God, through Jesus Christ—to Him be the glory forever! Amen."
Heb 13:20-32: "20 Now may the God of peace, who brought up from the dead our Lord Jesus—the great Shepherd of the sheep—with the blood of the everlasting covenant, 21 equip you with all that is good to do His will, working in us what is pleasing in His sight, through Jesus Christ, to whom be glory forever and ever. Amen."
Jude 1:24-25: "24 Now to Him who is able to protect you from stumbling and to make you stand in the presence of His glory, blameless and with great joy, 25 to the only God our Savior, through Jesus Christ our Lord, be glory, majesty, power, and authority before all time, now, and forever. Amen."
CONCLUSION: It is entirely appropriate to announce that we are praying in Jesus' name, but it is not commanded to do so, and we have many New Testament prayers in which it is not done. Therefore, we are not to bind the practice, lest we be found to be teaching as doctrine a commandment of men rather than of God.