Goodman had been a magazine publisher for several years before dipping his toe into the world of comics. He spent much of his career trying to tap into the zeitgeist of popular culture, and his magazine efforts were no different in that regard. Seeing the popularity of science fiction stories like Buck Rogers and Flash Gordon, Goodman launched a pulp magazine called Marvel Science Stories in 1938. The contents were fairly typical pulp sci-fi stories of the period, and the only reference I can find to any pieces that might be considered noteworthy is a story entitled "The Test-Tube Monster" by George E. Clark, which ran in the May 1940 issue, after the series itself had been retitled Marvel Tales. (The series was retitled again to Marvel Stories with the next issue.)
In any event, the "Marvel" name was in place before Marvel Comics #1. Whether Goodman was actively trying to build a sort of "Marvel" brand or he just happened to like the word is unknown.
But that's still only part of the story.
Something to keep in mind is that comics distribution in the mid-20th century was very different than it is today. There were a wider array of distributors in place, and a newsstand (there were no comic shops back then) could choose to order from any number of them. Which meant that they spent fairly little amount of time looking through all the lists of things they could order. Lots of titles from lots of publishers meant that a newsstand operator scanned quickly, sometimes completely missing titles and even whole groups of titles. Unless you had the name recognition of Life there was no guarantee your title would show up at the same newsstand even two months in a row.
One thing that publishers did to help counter this was to group titles together. You didn't order Superman, you ordered the group of comics that included Superman. Which meant that you also got, by default: Detective Comics, Green Lantern, World's Finest, etc. Even if you only wanted Superman.
Fortunately, magazines and comics were returnable, so there was little risk on the newsstands' part if a given issue didn't sell. You ordered Superman and got a bunch of other stuff too. Maybe those would sell, maybe not. If they didn't, you shipped the covers back to the publisher and got reimbursed for the whole issue. The actual contents of the issue would get thrown out, but comics were cheap and considered disposable entertainment, so no one cared. But what this set-up did -- from a publisher's perspective -- was get new titles out into the newsstands on the coattails of a proven seller. Kids came asking for "the comic with Superman in it" so you ordered that. Maybe you'd sell an extra few copies of Detective while you were at it.
Here's a page from the 1963 N.W. Ayer and Son's American Newspaper Annual and Directory. This particular page includes the listing for Marvel, where you can see a couple of the group breakdowns. (As a side note, too, you also see those bold numbers at the end? Those are circulation figures. But they're only listed for entire groups, not individual titles.)
(More on the directory and what it was here.)
Now, where am I going with all that? Prior to the 1960s, Goodman was publishing north of 30 comics a month. Some adventure, some Western, some romance... And you ordered them by groups. There was an adventure group, a Western group, a romance group... And what do you suppose the group with all the science fictiony monster comics was called? Marvel Comics Group.
If you ordered the Marvel Comics Group of comics, you got Strange Tales, Tales of Suspense, Tales to Astonish, Amazing Adult Fantasy... Lots of aliens and monsters and whatnot. And eventually, in 1961, something new called Fantastic Four featuring another big monster on the cover.
The superhero thing was a hit, so the creative folks at still-not-quite-yet-Marvel added more superheroes into the books that were in the same group as Fantastic Four. So we see the debut of Spider-Man in Amazing Fantasy, the debut of Iron Man in Tales of Suspense, the debut of Thor in Journey into Mystery... Lee was putting superheroes into books that were already being shipped out to the people who bought Fantastic Four. Or, more accurately, he was putting superheroes into books that were already being shipped out to the people who bought the comics group with other superheroes in it.
Eventually, the superhero genre took off and largely pushed out the romance and Western books they had been doing. The biggest comics they were publishing were superheroes, all of which were under the Marvel Comics Group. A little bit of directed branding later and Goodman had a new name for his company.