[jaddood]

As mentioned, it should be pronounced "rung," but in any case, removing the i and suddenly making it a word and pronouncing it in a very unexpected way is really pretty stupid. I think, if one's really insisting on using "ring" but without the i, at least call it "rung" not "rng" so that its pronounciation is clear.

If it's so important to have a "rng" instead of a "ring" then using its name in some example of its usage should probably be better.

[dramaqueen]

Well, words, terms, notations and conventions come super cheap in math. You can call/denote "rng" anything you want. You just have to let your readers/interlocutors know about your conventions at the outset which is a standard practice in math anyway. For another thing, "r(u)ng" to me it's no different from writing "colonel" and reading it "kernel" (historical accident aside) :) There's also "lieutenant" which is pronounced " leftenant" in UK.

[mangamadaiyan]

Lieutenant is "Leftenant" in other parts of the world (those with a British connection, of course) as well.