Besides that, the series is actually commonly known as Ginga Densetsu, or "Silver Fang Legend". Originally this just changed to the (series) qualifier instead but Ginga Densetsu would probably be the more accurate umbrella name and wouldn't require a qualifier.
Source for this? Even the various wikis (1, 2) just call it "Ginga".
Pretty much every entry in the series besides Ginga Nagareboshi Gin and TLW starts with "Ginga Densetsu". Ginga Densetsu Weed, Ginga Densetsu Weed Orion, Ginga Densetsu Riki, Ginga Densetsu Akame, Ginga Densetsu Noah... TLW and spinoff The First Wars are really the only post-Gin series to be branded as just "Ginga".
Pixiv tag 銀牙伝説 (Ginga Densetsu), while not the only tag in use, is used frequently for the whole series.
Silver Fang Network Wiki: "Today, it’s often described as Ginga Densetsu (ja. 銀牙伝説, en. Silver Fang Legend or Legend of Silver Fang)." Fandom wiki says the same thing, by the way.
Ginga Densetsu Akame's cover explicitly translates the series title (Ginga Densetsu) as Legend of Silver Fang, same thing with Noah. Both are branded as 銀牙伝説.
I believe the fan wikis just use Ginga because they don't have to disambiguate and there are a very small number of entries that don't brand themselves as Ginga Densetsu, but even the Silver Fang Network wiki acknowledges the use of Ginga Densetsu/Legend of Silver Fang as the series title. The fan sites also tend to follow very old fandom terminology that predates many of the series' entries.
Ginga (series) wouldn't be wrong, necessarily, but there's also strong official backing for Ginga Densetsu and it would more accurately represent what the majority of the entries are branded as, while not requiring a (series) qualifier.