tl;dr: Its etymology goes back to a German botanist named Leonhart Fuchs, plus an -ia suffix.
Fuchsia (OS) is named after a color which is named after a (genus of) plant. Like many plants and flowers, the plant's scientific name was given by some European guy after some other European guy, with an -ia suffix to make it a plant name. (Presumably in many cases because they couldn't fathom that indigenous people already had names for things, and so didn't bother to find out; there are plenty of plant names that are derived from indigenous names.)
| Plant | Named after | Named by | Native to |
|---|---|---|---|
| Fuchsia | Leonhart Fuchs | Charles Plumier | Americas, Oceania |
| Begonia | Michel Bégon | Charles Plumier | Asia, Americas |