I suspect that most of the folks hung up on "labels" have such a problem with terms because they don't really understand what the terms mean or, at least, haven't thought it through. They take a term and hang lots of detritus on it well beyond its meaning. They take a term that means "X" and claim it means "X+Y+Z" and thus it's a bad, bad term. In this instance, they ascribe extra meanings to "polyamorous" and insist that a new term is needed.
Polyamorous refers to having multiple, romantic relationships as a form of ethical nonmonogamy. One can identify as polyamorous, meaning one has a preference for having multiple romances at once, or one can simply engage in polyamorous arrangements without having any strong preference for such. Anybody--whether identifying as poly or not--can engage in poly arrangements or mono arrangements and simply say so. There is absolutely nothing about the term "polyamory" that precludes monogamous relationships.
I, who identify as polyamorous, can have monogamous or polyamorous relationships as I see fit. Neon Kaos, who does not identify as polyamorous, can engage in polyamorous arrangements or monogamous arrangements as she sees fit. The use of the term "polyamory" in no fashion affects any of that--it is a term that describes an approach to romantic relationships and doesn't preclude anything.
So "poly" is not some restrictive, prescriptive, proscriptive bogeyman of a word that imprisons people so that they need saving by another term.
I agree with this in principle. However, it seems people need labels to attach meaning to, especially people who think in dichotomies. I have never been polyamorous or considered myself polyamorous in the sense that I have never actually had multiple partners at the same time; but I have a partner who does. Some would say that I am a mono dating a poly, but that's not really true either. I think polyflexible is an appropriate description because I am also capable of having multiple partners and am open to the possibility but I personally don't intentionally seek or feel the need for multiple partners. I am indifferent really, because my identity and my capacity to "love" someone is not defined by partnership preferences or relationship practices.
Some could make the argument that I am actually polyamorous, however, because I do have multiple intimate friendships in which physical attraction is mutual, and physical affection (cuddling, holding hands, embracing, pecks on the lips) are mutual expressions of love and intimacy within our relationship, but we do not interact sexually or sensually, and there is no attachment or suggestion of expectations and/or desire for a "partnership" or sex; our relationship is defined only by a continuing commitment and desire to love each other as individuals implicitly embodied in our words, deeds, feelings, and behavior towards each other.
So, the question I ask is: do your relationships define you, or do you define your relationships?
The definition of omni as a prefix is:
1. all; of all things (as in "omniscient")
2. in all ways or places (as in"omnicompetent")
In this way I think Omniamory would be better used as a universal ideal in general; it has nothing to do with intimate/romantic/sexual/partnership. Rather, it could be considered a Spirit of Love; the commitment or capacity to love all beings in the purest sense, independent of personal relationship and interest. Whether this is actually possible, practical, or genuine is another matter that is subjective and not for us to judge in another's intention.
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