I almost posted this myself, but it didn’t explain the slow rise starting in 1935. You can’t tell by the graph for Steven until Capt America came out, but if you look at the percentage numbers, the rate was pretty steady from the 1920s through 1935, but starting in 1935 it crept upward every year by a noticeable amount. It broke out significantly after 1940, and perhaps Capt America was the major reason for that, but it looks to have started a few years earlier.
Were any adults reading Captain America in 1940?
Captain America was just a comic book. Superman was a super-splash, but it got its popularity from the cartoons, daily comic strip, and radio show, which meant millions of adults got to hear the name Clark Kent throughout WWII. Yet Clark lost ground as a name from 1938, when the comic debuted, through the 1940s. In fact, 1938 was higher than any time since. Lois also was higher ranked in 1938 than at any time since.
If Superman couldn’t boost Clark or Lois I have my doubts about any comic book of the time influencing any name’s popularity.
Not really, since the character wasn’t introduced until the very end of 1940. 
But, in seriousness, my understanding (possibly not entirely accurate) is that comic books were, at that time, largely an entertainment medium that was read by children. Adults (particularly educated adults) looked down on comic books as a childish thing.
Is it possible that the Steve Rogers character was a factor in the name becoming more popular with parents naming their baby boys in the 1940s? Possibly, though I suspect that it wasn’t a major factor.
Don’t forget about Stefon
My husband is a Steven, although his baptismal certificate shows Stephen. His mother has no clue (but that’s not unusual 
). Our son’s middle name was Stephen (pronounced Steven). I always thought Stephen was pronounced with a V and Stephan was pronounced with an F.
I’m a Steven with a “v” (which is what I always say when someone is asking for my name in some official capacity, like in a doctor’s office). But I have two colleagues orginally from other countries with variations: One Steffen from Germany and a Stefan from South Africa. Both pronounced with an “f” sound.
A musician friend of mine played and toured with Charlie Daniels. He was actually a nice guy. I was hanging out on his bus before a show at a county fair.
A local DJ stopped by to take pictures and get some 8x10s autographed. He handed Charlie a sharpie and asked him to sign it “to Steven”. Charlie asked how to spell it and the DJ said, “S…….T…….”, then Charlie rolled his eyes and grumbled, “V or PH”.