As the eBird person the Mysticete refers to, I can address this a bit.
I have written but not yet submitted a proposal for the NACC (North American Checklist Committee) to rename Common Gallinule. In short, I think the name is confusing for several reasons. First, Common Gallinule was used for the parent species in the past, making Common Gallinule (AOU 1957) and Common Gallinule (AOU 2012) totally different taxonomic concepts (sensu lato and sensu stricto, or Holarctic vs. Nearctic, respectively). Second, it leaves us with Common Gallinule and Common Moorhen looking almost identical but with names that imply a more distant relationship. Third, Common is just a poor modifier. Also, depending on your taxonomy, there are ~8 Gallinula in the world. Of those, only Spot-flanked Gallinule is a well-entrenched Gallinule (and that should probably change too). Although it does seem odd to have Gallinula called Moorhens and Porphyrio called Gallinules, I do see real value in having common names follow Genera. If Moorhen (e.g., Dusky Moorhen, Tristan Moorhen, Lesser Moorhen) is the predominant name for the Genus globally, I think the NACC and SACC should fall in line for their paltry two species.
Since having Common Gallinule and Common Moorhen seemed liked such a bad course, we opted for Eurasian Moorhen for G. chloropus for Clements/eBird. Retaining Common Moorhen would have led to hundreds of records being submitted to eBird as Common Moorhen, which then would have caused data quality issues as Common Moorhens were submitted from North America when the intended New World species was Common Gallinule (G. galeata). Common names DO matter, a lot, in citizen science efforts. We actually do dodge the issue of the example quoted below for the Moorhen/Gallinule (i.e., there is no option to submit Common Moorhen in eBird), but it is an issue that arises in other cases, such as Common Snipe.Simply causing people to stop and say "Wait, why are the names different" (as with this thread) itself is important to data quality.
For G. galeata, I really like the proposal by The Sound Approach team to use Laughing Moorhen for G. galeata. This gets at one of the main differences between Old World and New World species and also following the subspecies name, cachinnans, for one of the New World forms. So I would hope that global authorities can converge on Laughing Moorhen and Eurasian Moorhen, and leave Common Moorhen and Common Gallinule behind.
Along this same vein, I did recently submit a proposal to NACC not to adopt Xantus's Murrelet for the newly split (I think the proposal passed) sensu stricto Synthliboramphus hypoleucus. This was especially dangerous since the scientific name would not change either and we would be left with sensu stricto and sensu lato versions of Xantus's Murrelet. I proposed Guadalupe Murrelet.
Along the same vein, the recent NACC Gray Hawk split raises the same problems. In this case there is no good alternate common name for the northern species Buteo plagiatus, and since the scientific names will change and the North American form will retain stability in English name, perhaps it is less of an issue.
But overall I feel it is important for taxonomic authorities to try not to use the same English name for parent species and daughter species, since confusions (Common Gallinule, Snowy Plover, Common Snipe, Black-billed Magpie, Black Scoter...for some recent Nearctic examples) are sure to arise. With eBird we run into problems when people submit from listing software using only scientific names, since eBird then matches to the appropriate common name. We continue to get occasional Eurasian Wrens, Common Scoters, and Common Snipe coming from users who have not updated the taxonomy in their listing software.
So here's a call to consider English names carefully and avoid using the same one for parent and daughter species!
In some of those cases however the common name of the bird was only ever used in North America really, i.e. Kentish Plover and Black Scoter. So birders reporting species can still say they saw a Snowy Plover and report it on ebird, without much worry that they actually meant something else.
In contrast, If I log my sightings onto ebird or send a trip report out to a listserve, by common moorhen do I mean I saw a rare vagrant of the old world taxon, now recorded in Alaska and probably added to the the next edition of the ABA checklist. Do I mean Common Gallinule as currently defined? What if I have been birding for a couple of decades and still use older names. What about when I go overseas, will my trip lists all report Common Gallinule?
If anything, if you look at the response to the Winter Wren situation, I think the confusion regarding what people mean by Winter Wren makes clear my point.