There's a slime called マゴノテ:
Literally, this means "back scratcher" in Japanese.
See the resemblance? The explanation for this slime's name could be as simple as that. However, my research uncovered a little bit of a story behind the Japanese word.
The kanji form of マゴノテ is 「孫の手」, which means "grandchild's hand."
If you go a little deeper - according to Wikipedia, the word was originally 「麻姑の手」(まこのて）. "Mako" (麻姑) is the Japanese version of the Chinese deity Magu. Magu was a beautiful female immortal who had some association with the elixir of life, and was known for possessing long, claw-like fingernails.
There's apparently an expression - 「麻姑掻痒」(まこそうよう) - "Mako scratches the itch," which means something like "everything going according to one's desires."
Anyway, the word for "back scratcher" started off as a reference to the hands of Mako, which would be perfect for such a task. It seems "Mako" eventually morphed into "Mago" (grandchild), though, owing to the fact that the back scratcher's "hand" more closely resembles that of a child than a claw.
This brings us back to the eponymous slime. If I were officially translating the game, I'd be sure to clarify with the developer on this point. However, in my judgement he's referring to both the physical similarity between the slime and the shape of a back scratcher and the divine association of the goddess Mako. It seems that Mako had something to do with the elixir of life; meanwhile the slime's special ability is that when damaged it splits into two, restoring itself in a fashion.
Rather than translate its name as "Back Scratcher Slime" I thought it better sounding to stretch a little bit and kind of localize it as "Goddess' Hand." The meaning of the name may not really be clear to English speakers, but then there are tons of references to ancient religions and lore in all kinds of games (especially JRPGs) that casual gamers may not pick up.
Back Scratcher Image Source: Rakuten
Magu Image Source: Wikimedia