"Allamagoosa" is just an obsolete way of saying "thingamajig" -- a word you use to refer to something when you don't know what it is. The word appears twice in the story (other than the title).
In the first one, the captain is discussing what the "offog" might be with his crew.
"Because it's typical of the baby names used for your kind of stuff. I'll bet a month's pay that an offog is some sort of scientific allamagoosa. Something to do with fog, perhaps. Maybe a blind-approach gadget."
"The blind-approach transceiver is called 'the fumbly,' " Burman informed.
Notice that "gadget" is considered even more specific than "allamagoosa" here.
A little later, the captain orders a crewmember to make something and call it an "offog":
"All we need do is concoct an imposing allamagoosa and tell him it's the offog."
He's trying to placate the the head inspector Rear Admiral Cassidy who's a stickler for accounting for everything on the manifest.
This may be one of those GI-created words like fubar. Google ngrams viewer has a spike for "allamagoosa" during World War II (there are no book search results behind it).
A Stephen King message board user named GNTLGNT gives a potential Miq'maq etymology:
...the genesis of the "name" may be from a short story written by Eric Frank Russell. The story, published in 1955, is called "Allamagoosa," which is a nonsense word that one would call something when you don't know what it's actually called...or a derivative ...possibly even a corruption of a'qîti-mntuit Animate Intransitive Verb meaning demidevil....
but IMO it's pretty weak. King used the word "Allamagoosalum" in his story "Uncle Otto's Truck" but could just as easily have gotten this word from the Eric Frank Russell story.
FuzzyBoots points out that this story is a sci-fi retelling of the old Royal Navy yarn "The Shovewood" - this would be analogous to titling EFR's story "The Offog".