🔼The name Rimmon-methoar in the Bible
It's not clear whether Rimmon-methoar (or rather actually Rimmon-hamethoar) is actually a name or not. The authors of the King James thought it was, and so did those of the JSP and Young translations. More recent versions (ASV, NAS, NIV, Darby) only print Rimmon and translate the methoar-part as part of the narrative.
That narrative occurs in Joshua 19:13, where the borders of the territory of Zebulun are discussed. After going through Gath-hepher and Eth-kazin, the border went to רמון המתאר הנעה, or rimmon-hamethoar-hanea. Although this term has all the qualities of one big name, the final part is commonly interpreted as the name Neah and the first part as the familiar name Rimmon. What the middle part is remains unclear.
🔼Etymology of the name Rimmon-methoar
The second part of our name Rimmon-methoar may be a certain kind of participle of the root verb תאר (ta'ar), meaning to draw an outline:
Prefixed to the second and the third part of the whole term rimmon-hamethoar-hanea is the letter ה (he), which in this case works as a particle of direction or description, and which is very common in names of the formula X-of-Y.
The Rimmon-part of our name means Pomegranate, so if rimmon-hamethoar is a name, it would mean something like Pomegranate Of The Outlining, which doesn't make a lot of sense but could perhaps be construed as a poetic way of denoting, say, a rock in the shape of a pomegranate. Also possible is that hamethoar-hanea was a certain expression, which was lost over time, perhaps meaning something like "forms and wanderings" and denoting the outskirts and regions of the town called Rimmon.
As stated above, most modern commentators and translators see the methoar-part as part of the narrative, but that's actually hard to defend. This participle occurs only in Joshua 19:13, while the descriptions of the tribal territories go on for chapters, which seems to suggest that the author is saying something that doesn't get said anywhere else. It's a mystery that perhaps in the future might be solved with greater authority than anybody's guesses.