Cantleave(wife) ?
Jesus told us to ouse "Our Father" to instill in us the understanding that we need to build a personal relationship with God, through Jesus.
We must first KNOW Jesus to KNOW God, but the vital point is that knowledge must be personal, loving and affectionate.
We are only sepculating on what we think Jesus may or may not have done and whither he used God's Divien name or not is far less important than Jesus actual words telling us what to do.
We know Jesus actual name in the sense that we know his Greek name, But we don't know that of God's name for there is NOWHERE stated God's full name, at best we can speculate, but why do that when Jesus made it clear HOW WE should pray?
I truly have no problem with anyone using the term Jehovah as one of his possible names, a name they choose to use, I do have problems with anyone saying it is the TRUE and ONLY name of God because we do NOT know that.
As for the OT God and the NT God, yes there is only One God and Jesus worshipped this one God, I just have serious doubts that God is the one WRITTEN about in some of the OT passages.
My God is the God of the New testament, the God of the New Covenant and my Lord and Saviour is his Son Jesus Christ.