> *particle that is emitted from an alpha decay isn't actually called a He atom”

“Because they are identical to helium nuclei, they are also sometimes written as He2+…” [1].

[1] https://en.wikipedia.org/wiki/Alpha_particle

You should really have posed that as a "I don't know anything about this so I'm confused" question.

He2+ is not a helium ion, which is very reactive. It’s not a helium atom, which is inert.