Biblically speaking, should the name of Jesus be omitted from Christian prayer for pragmatic reasons?

I was once asked by a Moslem family, with whom I had become aquainted, to attend a memorial gathering for their father at the grave side, one year after his death. At the end of our time there they asked me if I would pray, and I said that I would count it a privilege but said that I could only pray in the name of Jesus and if they found that unacceptable I would understand. They were happy for me to pray in my usual way, and realising that the only blessing this family could be blessed would be to know the Truth and come to Jesus. I went ahead and asked the LORD to bless them and lead them into all Truth. Praise God most of that family are born again and walk with Jesus, His Name is indeed the Name above all names.