Theism,monotheism, polytheism, and henotheism are all general terms which make generalizations about a given belief system. It is not necessary to suppose that the general descriptive term would have to be specific and particular to a given belief system. In other words, a general term will not and cannot specifically define a specific belief system.
Example: There are many different kinds of theists. a muslim is theist, and so is a practitioner of Talmudic Judaism, and so is a practitioner of the Hopi religion. But major details, minor details, nuances and praxis are all different for each of those belief systems, even though they are all under the very general category of theism. A Muslim could not logically deny being theist just because a practitioner of Talmudic Judaism also makes a claim to theism. All muslims are theists, but not all theists are muslims. A practitioner of Talmudic Judaism who applies the term theist to himself would not be worried that he'd be giving deference to a Muslim. A talmudic Jew is a theist, but not every theist is a Talmudic Jew.

Since henotheism is a fairly recent term (and not a very commonly used term), its application is still being explored and worked out. Had Max Müller studied the Nazarenes, I don't see how he could have avoided classifying the Nazarenes as henotheists.
True, some henotheists (not Nazarenes) swap their supreme deities depending upon circumstanses or whatever,so that is one thing that makes other henotheists different from the Nazarene henotheist. Also, because the Nazarene henotheist's view is distinctly familial and more particularly patriarchal, those are the main qualifiers that make the Nazarene's henotheism different from other henotheists. Patriarchal henotheism perhaps. If one wanted to go the greek/latin route of inventing a word, patritheism, would probably be most accurate for the Nazarene-- it'd certainly be a much more specific term than henotheism.

I don't disagree with anything you have written here - my point is that would it not be simpler, more practical and save time if we used a new term to avoid endless theological debating and the usual litany of false charges that are leveled by monotarians and others bent on picking a fight? Then we would not have to be sidetracked by academic debates and could instead focus on what we're really about, viz. sharing the Gospel/Besorah. Patritheism is certainly a good label - I like that - and Patriarchal Henotheism is a useful qualifier. But given the abuse of the 'patriarchal' term these days an extra qualifier like Echad Patriarchal Henotheism might also be useful. Finally (another reason I dislike the 'henotheism' label) is its association by sound with Hedonism: we must not also have a term that will satisfy the academics but also strike a resonant cord with the 'masses' without unnecessary alienation of other believers. Words are powerful things because of their associations in people's subconscious. I think that is why the Echad Doctrine of the Elohim-head/Godhead has always rested most comfortably with me. What's needed, then, are two things:

1. A simple, popular term; and
2. A precise academic qualification

If we can solve this, I think we will have done well. As far as the popular term is concerned, unless we coin that early on, people will coin one of their own.

I guess in using the already existing term henotheism, i was attempting to find some general category that already had some sort of academic precedence, because Patriarchinity was already a newly invented term. (On one of the networks, there was someone who was just beside himself because he couldn't find patriarchinity in the dictionary ; o )

Given the fact that henotheism is a general term, which has many different applications, just as monotheism is a general term with many applications, any Jewish or Christian monotheist who objects on the grounds that henotheism is not specifically defining the Nazarene faith, is not being consistent with themselves, since they use monotheism to make a generalization about their own belief system even though there are other pagan religions that are classified under monotheism. So if they object, they are using different weights and measures (maybe even unawares).

No matter what terminology and no matter what line of arguments one uses, monotarians will pick a fight.

I agree that more specificity is always more desirable because of the unfairness of the detractors, but specificity is not always practical since it can end up being quite a mouthful.

Ultimately, one wants a succinct way to say:
"I believe in the Patriarchial Family of Elohim:
Divine Father YHWH super-ordinate over all,
His Divine Son Yehoshua, subordinate to Father YHWH,
The feminine Ruach HaQodesh (subordinate to YHWH), who is 1 and/or 7, who is Yehoshua's Mother(s),
Amein"

But a single word will always fall short of completely summarizing all the details and nuances of such a creed.

That summary has all the flavour and cadence of an extract from a new Apostles Creed - lol I might incorporate it.

I agree entirely with you.