According to early 20th century scholarship (see the classic Gesenius' Hebrew Grammar, pg 249):
It can hardly be doubted (but cf. h, Rem.) that the (locative) termination ־ָה is a survival of the old accusative termination a, and that וּ in certain compound proper names is the old sign of the nominative.
So (according to 1910 grammarians), Yirmiyahu and Yishayahu and Eliyahu are nominative forms, while Yirmiyah, Yishayah and Eliyah are not. A noun that is in the nominative case is the actor of the sentence, usually correlating with what we call the "subject" of a sentence.
Thus, neglecting case suffixes, these prophets all have the short name of G-d (spelled Yod-hey, and pronounced "Yah") at the end of their names. The full Name Of G-d is spelled with a Yod-hey followed by a Vav-hey. We Jews do not have a tradition as to how it was pronounced in antiquity, but modern linguists have hypothesized that it is said something like "Yahweh" (see Wikipedia).
As for your concern about folks knowing G-d's Name, I really don't think that G-d means the word we use for His Name. "Name" can mean "character" or "reputation". I think that when we speak about the world knowing G-d's name, we are primarily saying that we want folks to recognize G-d as the Sole Creator, King and Master of the Universe. We don't particularly care about how people pronounce that. (NOTE: If anyone can suggest sources here, it'd be appreciated.)