I see nothing to get terribly upset about when it comes to various possible names for deep-sky objects, as long as the proper catalog IDs are also provided up-front (and as long as no one claims that name is somehow "official", as it usually can never really be). There have been multiple names for some of the most promient deep-sky objects way back *many* decades ago, so it is to be expected. M33 went by several names like "the Pinwheel Galaxy", a name it shared with both M101 and M99. "The Spindle Galaxy" also referred to more than one object: NGC 5866 and NGC 3115. "The Little Gem" has always been NGC 6818 to me ever since I first heard of it many years ago (and SIMBAD responds to that name with the NGC 6818 ID), so I don't know about it being associated with another nebula. As long as someone says, "NGC 6818" or "the little planetary north of Barnard's Galaxy", I'll know what they are talking about.
I have sort of "named" a few myself for my own use, and one or two of these names actually have caught-on a bit with others. One name's appearance sort of caught me by accident, as during one observing report, I mentioned that the fine planetary nebula NGC 3242 in Hydra at very high power looked a little like the old logo for the Columbian Broadcasting Network ("the CBS Eye"). Now, I see that the SEDS list has that CBS Eye name listed for that very object (who'd a thunk?)! Another one I ran into when looking over the old Palomar Sky Survey plates on laserdisk (yea, that kind of dates me a little, as it was 1989) and noted one planetary nebula that looked like a pair of headphones or earmuffs. That one (the big planetary PNG 164.8 + 31.1 (or Jones-Emberson 1) in Lynx) I called "the Headphones", and after I finally tracked it down in my 10 inch with filters, I did write about it both in our club newsletter and on-line. Even though it is a fairly faint and somewhat obscure target, I have since heard the object referred to by that name serveral times on-line, so maybe a few people do think it may look a little like that common audio appliance. Around 1970, someone in our club (a certain Lincoln East High School student) who was viewing the fine open cluster NGC 6939 in Cepheus in an old RV-6 called it, "The Seacrest Cluster", as it resembled a set of stadium lights at Lincoln Nebraska's Seacrest Field. That name never caught on with me (I didn't live in Lincoln), so in my notes, I called it "The Right Angle Cluster", for the row and central column of stars that forms a very visible right angle in that group. When doing my first nebula survey with my 10 inch and my "new" OIII filter (around 1988), in Cassiopeia, I ran into a large faint complex of nebulosity plotted but unlabled on the old Skalnate-Pleso atlas ("Atlas of The Heavens" Atlas Coeli 1950.0) that had three arcs running away from a box-like mass. Not knowing what it was at the time, I called this complex, "the fingers", as on the atlas, it looked like fingers extending away from a hand, although again, this name was more for my use than someone else. It wasn't plotted on the 1st edition of Sky Atlas 2000, so I kept that "name" as its primary identifier for over a decade until I finally tracked down a catalog that had it. Now, while I "officially" refer it as (Sharpless) Sh2-157, "the fingers" still sticks in my mind whenever I go looking for it.
For a lot of the "common" names, the list below is fairly complete:
Otherwise, I will only quote the Bard; "What's in a name? That which we call a rose, by any other name would smell as sweet;"
Enough said. Clear skies to you.