This is a very slangish word among young people.
Literally, "run-ner" I think - a person who runs
for his/her boss. A person available for his/her
boss to do anything for him.
"Bring me a cup of coffee." "Right away, boss."
"Hit that rascal." "Yes, boss."
Are there any such new words in English?
Thank you.
There are no new words for this in English (that I know of), but we do have an old term; a 'yes-man'.
A very common slang expression in Australia is; 'a**-licker'.

I'm sure there are other words and expressions.

By the way, thanks for the new Japanese word. :-)

[note to MrM; I think we both looked at this at the same time]
A gofer?
Students: Are you brave enough to let our tutors analyse your pronunciation?
Gofer this, gofer that go for this, go for that ('go for' can mean 'go and get')
(Funny, I always thought it was a gopher.)

How about a grunt, or is that limited to use in the military?
A boot licker?
Teachers: We supply a list of EFL job vacancies
I think it's also called a FLUNKEY or FLUNKY.

flunkey or flunky /'flHEkN/
noun (flunkeys or flunkies)
1 a uniformed manservant, eg a footman.
2 derog a slavish follower.
3 N Amer a person doing a humble or menial job.
[18c: possibly from flanker someone who runs alongside.]
And by the way I think GOFER and GOPHER are actually two different things :

gofer /'goLfB(r)/
noun, originally N Amer, especially US in an office or on a film set: a junior employee who runs errands.
[1960s: from go for.]

gopher1 /'goLfB(r)/
1 a small burrowing N American rodent with a stocky body, short legs, large chisel-like incisor teeth and two large external fur-lined cheek pouches.
2 a ground squirrel.
3 N Amer any of various other burrowing animals, eg a burrowing tortoise, a burrowing snake and certain salamanders.
verb (gophered, gophering) intrans, US to carry on small-scale mining.

And GOFER definitely sounds like the best match so far...