If we are to pray to the Father, through the Son, in the Holy Spirit, do my prayers become null and void when I am praying to Jesus and end it with “in Jesus' name, amen”?
Jesus is the name given to us by which we know and approach God at the most intimate and personal level. Keeping our relationship to God personal is what Jesus had in mind even with regard to baptism when He taught us to baptize in the name of the Father, the Son and the Holy Spirit. "Jesus" is the personal name of the Father, Son and Holy Spirit!
When you, as a follower of Jesus, pray to the Father, the Son or the Holy Spirit, whether you use Jesus' name or not, God knows who you are talking to. He's not interested in correct formulas; He's interested in you! The role of the Holy Spirit is to direct us to Jesus, and Jesus always directs us to our heavenly Father. That's why we pray "in Jesus' name": "And whatever you do, whether in word or deed, do it all in the name of the Lord Jesus, giving thanks to God the Father through him" (Col. 3:17).
“God the Father” is a description, not a name. It’s accurate, but it is not personal. It’s like saying “Bob the teacher” or “Margaret the librarian”… accurate, but not personal. Likewise, the Holy Spirit is descriptive of God in His character (He is holy) and of His nature (He is Spirit). That’s like saying “the good-natured man.” It describes someone’s character (good-natured) and his nature (human, male).
Even in the Old Testament, when God revealed Himself by name to Moses at the burning bush—“Yahweh,” i.e., “I Am Who I Am”— (Ex. 3:14), He gave a name which described His relationship to Moses and the Hebrew people: “I Am the One who always exists, and who will be with you always.” This name was, and is, personal. In fact, it was so personal, so holy, that the Jewish people would not say it aloud or even spell it out completely, but only use the consonants: YHWH.
Consequently, when Jesus declared to the Jewish people of His day, “before Abraham was born, I am!” (John 8:58), they understood Jesus was identifying himself with God and they attempted to stone him to death for blasphemy. In effect, Jesus was saying, ‘I am the great “I Am” in human form.’ God in flesh—the final and complete revelation of God that would provide salvation not only to the Hebrew people but to the whole world.
"Salvation is found in no one else, for there is no other name under heaven given to men by which we must be saved" (Acts 4:12).