The question that always arises when one prays on such occasions is how one should frame a public prayer -- that is, when you pray in a public setting do you see yourself offering a blessing on behalf of God as you see God, or are you carrying the prayers of all the people to the divine?
This issue will likely emerge once again when the already heavily criticized Rick Warren takes the podium and offers his invocation at the Barack Obama inauguration. The critics are already after him, believing that Warren's likely use of the phrase "In the Name of Jesus" should disqualify him. Now the invocators/benedictors at the GW Bush inauguration used just such a phrase and it raised the hackles of many. The response is that when one prays in public, one should pray as one always prays, in accord with one's religious views.
As a sidebar to this discussion, I want to first say to those who are clamoring for a rescinding of this invitation -- don't get your hopes up. It ain't going to happen!!! If he were to comply he would not only show weakness, he would likely inflame the passions of others. As to the use of the phrase, "in the name of Jesus," I think we must first give Rick Warren the benefit of the doubt that he will pray in a way that recognizes the nature of the event. Maybe he won't, maybe he will. We won't know until January 20th.
Now, as to the prayer. I've taken the view that when you are praying in a public setting like this, you are leading prayer. Thus, you need to be cognizant of everyone present. That means that you should give your prayer in a way that would allow everyone present to give their affirmation, their Amen. If you're Jewish or Muslim, and I pray in the name of Jesus you will find it difficult to give your Amen.
I know that even here there will be those unable to participate, but I think you have to be as broad as possible in your appeal. At least that's how I'd do it.