Yes, without assigning God a personal name, he takes on a distant, impersonal character. The whole "we don't know how it was originally pronounced in ancient Hebrew" argument is rather weak if you ask me. I consider there to be only two logical arguments against using the divine name:
1. - Having to use a "differentia" implies that it is necessary to distinguish him from other gods, as if to acknowledge the existence of rival deities, which could be construed as disrespectful to his exclusive Godship. He is THE God, so there's no need for qualifications.
2. - His name is not recorded as having been used in all the extant copies of the New Testament.
The first is probably the stronger of the two. I believe his name was used by Jesus and the primitive christians for a number of reasons. For one, Jesus repeatedly said that he made his father's name known..surely he wasn't claiming that his father's name was "father" or "abba", as those were merely titles. Also, I believe it was Paul or one of the apostles who said that the christian congregation was the fulfillment of the prophecy whereby Jehovah would "take out from the nations a people for his name" (I'm not sure if that's how it's worded in English). Third, whenever Jesus or the new testament writers quoted from the Hebrew canon, they surely would've quoted their sacred texts accurately, and they would have used the divine name.
I think the reason why it isn't specifically recorded in the gospels that Jesus used the divine name Jehovah, is most likely because of the prevailing superstition of his day in the culture in which he was raised, regarding the use of the name. Maybe he was sensitive to the cultural custom of avoiding the use of the name, and rather than shocking his potential followers or stumbling them, he politely refrained from using the name. Or maybe he constantly referred to God as the "Father" to emphasize that role played by God, that quality of a loving, personal father who we could turn to for comfort, (in stark contrast to the sometimes cruel, violent, jealous and vindictive God of the Old Testament) and to emphasize his unique relationship to him as the only-begotten son of God. He wanted to reiterate how he was the Son of God, a divine being, the firstborn of all creation.
Personally, if I believed in the power of prayer, I would refer to God by his name, Jehovah or Yahweh or Yehoawah, or any other form we might imagine to be closest to the original form. (There is evidence that his name contained three syllables, meaning that "Yahweh" is not a close approximation of his name, but probably something closer to "Yehoawa"). It makes him seem more real, and consider the meaning. If the society's etymological research is anywhere near correct, and I hope it is, then per what I've read, Jehovah is taken from the verb root which means "(to become, or come to be", and it is the causative form of the verb, meaning that "he causes to become"...I personally think this is simply another way of saying "The Creator", as it means "he who causes things to come into existence". So to me, the most probable meaning of the name means "Creator". And if I prayed to anybody, it would only because they created me.