Vasa wasn't named after the royal house, it was named after the vase[0] on the heraldic symbol for the house of Vasa[1]. A vase is probably best described as a fasces. Äpplet was probably named after a globus cruciger[2], or "national apple" (riksäpple), part of the regalia of Sweden.
Gustav was known as "Gustav Eriksson" in his day, "Eriksson" being a patronym. Family names wasn't really a thing at the time, as coat of arms were. The form "Gustav Eriksson Vasa" first appears in the 17th century and simply "Gustav Vasa" isn't used before the 18th.
Tangentially, there is an interesting connection between Scandanavia and the Mac: the command key symbol, AKA Saint John's Arms (among others). When I've visited Sweden, it's all over the countryside, on signs marking places of interest.
Another similar tangent: Rambo got his name from the Rambo apple, which in turn got its name from Peter Gunnarsson Ramberg who took the name from Ramberget in Gothenburg.
[0] https://sv.wikipedia.org/wiki/Vase_(heraldisk_symbol)
[1] https://sv.wikipedia.org/wiki/Vasa%C3%A4tten#/media/Fil:COA-...
[2] https://en.wikipedia.org/wiki/Globus_cruciger