For starters, what is prayer? People all over the world pray. I would think prayer, at the simplest level, is the communication of a person or group of people to an entity, higher power, being or group of beings, or some other object of worship or faith. In addition, I think the person or group offering the communication believe that in at least some way the communication will yield a result.
The Triune God of the Bible, that is, the Old and New Testaments, is living and engaged with his creation (for clarity he may also be identified as Yahweh). He is omnipresent and therefore hears and knows all communication--in speech, thought, and action--of all people, whether they believe and worship him or not. He is sovereign over his response and personal revelation and can choose to communicate with the person praying or not; he can take action or not, whether they are intentionally praying to him or not.
For the purposes of this post, I will call Christian-prayers those communication attempts made by Christians to communicate with the Triune God. Christian prayers are generally understood as being made through, and in the name of Jesus Christ. The person praying a Christian-prayer professes Jesus as Lord and Savior; fully human and fully God; concieved of the Holy Spirit; crucified, dead, and risen as a propitiation of our sins; and part of the Triune God; however, there is some room for a person to not fully understand these aspects of Jesus and the Triune God, but they may not deny them.
Many people offering prayers are attempting to communicate with Yahweh even if they do not know or believe in Jesus, especially the Jewish people. These prayers are not specifically Christian prayers, but this does not mean that God does not hear them, and potentially even answer them. Before a person believes in Jesus, he or she may pray for greater faith to believe or for help understanding the Scriptures. God, in his sovereign ways may very well answer these non-Christian prayers by his common grace and love for mankind. The man who for the first time cries out to Jesus, "Lord, I can do nothing; save me," was not a Christian when his cry started but in fact was regenerated to new life, through grace, by the very act of this "non-Christian" prayer.
However, when a person prays to anything or anyone other than Yahweh (which includes Jesus), he or she is praying to a false god or false idol. God still hears these prayers but they are not pleasing to him considering that throughout the Bible we are warned not to worship false idols. In fact, Paul warns in 1 Corinthians 10:19-21 that food sacrificed to false idols is actually being sacrificed to demons. Prayer to false idols could, like the sacrifices, be made to demons.
In the case of public prayers or invocations, it is not absolutely necessary that specific names be mentioned, but it is a better witness if the prayer is clearly addressed to the God of the Bible and absolutely prayed in Jesus' name. This cannot always be the case given our society. God will know the intentions and hearts of those saying, engaging, or agreeing with the prayer. Now, a prayer that is vague in name is one thing, a prayer made to a false idol is another. Never, should a prayer be made to a false idol or an incorrect identification of God.
To provide some practical application, I have some in-laws that are LDS (Mormon). To be clear, I do not believe that the LDS god is the God of the Bible, therefore, he is a false idol. I do not believe that their understanding of Jesus is inline with what the Bible teaches about Jesus (and it's really all about Jesus!); therefore, the "Jesus" they understand is not the same as the Jesus of the Bible. However, when we are together for a meal, a prayer is offered before we dig in. When one of them prays to their "heavenly father," I can pray in my heart to Jesus or my Heavenly Father, and that is okay. Or I can pray a different prayer in my mind. But I am always intentional about the object of my prayers--Jesus the Living God. And when I am asked to pray (which is almost never), I have two options. The first option is that I can choose to cause a problem by intentionally praying in such a way that becomes offensive to them. This could hurt my future witness with them and make for poor family relationships. [I understand that should one of them read this post, there will be challenges to their faith, but they won't be made in front of the rest of their children or the rest of the family. If I am challenging your faith, I am always happy to discuss this with you.] The second option is that I can choose to pray in such a way that affords them the opportunity to join in my prayer to God or--as much as I want otherwise--they can place their false idol as the object of their prayer. This is not to say that I am compromising and praying in some way that is not correct to God. For example, they believe that addressing their deity as "god" is taking their lord's name in vain. They do not even do it this their prayers. While I am okay to address God with the title "God," I am also okay to call God "Heavenly Father" or "Lord." These latter two terms are not offensive to them, which makes these titles a more appropriate choice. They pray using King James language, feeling it holds greater reverence. I do not do this because I am not practiced in this vocabulary and will probably unknowingly make up incorrect King James words. But more importantly, it is because I feel that coming before God as something other than myself is fake. I believe God knows us better than we know ourselves, is approachable, and loves us as his children; therefore, I will not pray as if I am trying to appease him or superficially respect him with my language. (In many ways, how I pray with these LDS in-laws can be a witness of my love-relationship with my Creator.)
In conclusion, I must say that I believe all prayer should be Christian prayer. Jesus is the Way the Truth and the Life, creating the only bridge to the Father. Any other prayer to any other god, higher power, or anything else is a waste of time and offers no hope of salvation. The Bible declares this to be true, and in this I am certain.
*This photo is by David Shankbone and is registered under a Creative Commons License.
**This post was, in its entirety or in part, originally written in seminary in partial fulfillment of a M.Div. It may have been redacted or modified for this website.