I think one thing that might help in the discussion is to understand that 'in the name of' does not equate to the designation/title given a person to address them by. Jesus, Allan, John, etc...
'In the name of" means by or according to the authority of. However it should not become the tag line for the end of prayer. It should be stated with understanding of what it entails. I have found however that many do not even know this. They presume the end of the prayer should be much the closing of an official letter, complete with closing signature.
Surprisingly, you don't even need to 'say' the words to pray in His authority. This is about understanding and confidence that we have to approach the thrice Holy God. Not only in knowing it is His authority but that the one who comes in His name should be a proper representive of Him in word and deed. However stating the 'name' or authority in which you are speaking helps to acknowledge through who's authority you are praying so that others know this as well.
So whether to the Father, or the Son (Jesus help me), or the Holy Spirit (Holy Spirit open my eyes and guide me).. all of these are God and while distinct they are also one. Yet I will defer to scripture on this and state that Jesus does show us a "Model" prayer after the disciples as Him to pray and He states we should pray in such a manner: Our Father...
Why, because at the end of it all, it will all go back to Him. To Him, Jesus will give the Kingdom back to. From Him, all blessing flow. To Him, belong the Power and Glory forever and ever - Amen (so be it). Additionally, we see Paul through the moving of the Holy Spirit states that we 'cry Abba, Father' (Rom 8:15; Gal 4:6), in like manner that Jesus Himself did as well (Mark 14:36).
So while it is not inherently wrong to pray to the others of the Godhead, they themselves look to the Father and are our examples. For the Son sought to do only the 'will of the Father" while on earth.. The Spirit prays for us, since God knows our hearts AND knows the mind of the Spirit because the Spirit intercedes for the saints according to the will of God.
While all are God and equal, Jesus and the Holy Spirit still yeild all things back to Father.