On Earth-415, Steve never went into the ice, so it's possible that he and Peggy's daughter might have been born before the "other" Sharon - if the latter even exists in that universe. (You can place both Sharons on the same team in the game, though I don't think they are from the same universe.)
In this instance, there could be plenty of alternate name options which Earth-199999's Steve could consider, so long as the overall concept of his and Peggy's daughter inheriting the Captain America moniker were to be put in place.
On a semi-related note, If I recall correctly, there's at least one DC comic timeline in which Bruce and Clark were active starting in the 1930s, and where successive generations of Waynes and Kents passed on those respective capes.
I was under the impression that the first animated What If...? story on Disney+ will be along those lines.