The description of God as a three-headed or three-bodied entity is actually one of those things promoted by the Watchtower Society as a red herring used in its stand against the Trinity. While there is artwork that uses such imagery in regards to the Trinity, such imagery and the Watchtower description of it has very little to do with the actual doctrine.
One thing I fret is that people take so much of what the Watchtower has taught them and still cling to it as accurate, even after they have left the organization. Whether people who leave the Watchtower eventually adopt belief in the Trinity or do not (everyone should make up their own minds and treated with respect whatever position they choose), as a religious historian I must protest the way Jehovah’s Witnesses have misrepresented the Trinity teaching. Though I am not going to here promote or advocate such a doctrine, I should point out that what JWs say about it and what citations and quotes they print are very incomplete and misleading.
Religions that believe in the Trinity have a concept of three persons making up one God, similar as to how Genesis describes a man and a wife making one flesh or how parents and their children make up one family unit. In the same way that the human mind cannot conceive that God had no beginning, Trinitarians also believe it is the same regarding this teaching, that it is a “truth” that cannot be fully explained in human terms.
From a strict apologetic approach, the reasoning used by Jehovah’s Witnesses in their refutation of the Trinity doctrine consists of a misrepresentation of a basic tenet of this teaching, namely that it defies explanation. To therefore argue that the doctrine is confusing or doesn’t make sense or isn’t found directly in Scripture is moot; Trinitarians also agree to the same things.
This approach is referred to as the “straw man” technique. Here the Witnesses teach that they have the “truth” because they can prove that the Trinity defies human reasoning. When the Witnesses prove that the doctrine defies human reasoning they claim this as an earmark that they have the “truth,” when in reality they have just argued in support of the Trinitarian’s claim that the Trinity defies human reasoning.
To the unsuspecting lay person who never learned the basics regarding historical Christian development and the Trinity doctrine, the Witnesses look impressive as they do this trick. But in reality they’ve just knocked over a “straw man,” a moot argument that proves nothing but the exact same thing Trinitarians believe.
Again, please don't misconstrue this as a declaration of my personal beliefs or a promotion of the Trinity, but after reading many of the comments on here for some years before I finally began posting recently, one thing I have noticed, even in myself, is that the insidious techniques of programming the Witnesses employ often do not get entirely unlearned, and this often leaves people still misunderstanding many things in the world, especially in the world of religion.