The New Latin genus name uses Greek pieces describing a good covering, referring to the cap over developing buds.
L’Héritier introduced the botanical genus name in 1788.
Sources
- Merriam-Webster: eucalyptus
The name refers to the bud cover; the note dates introduction of the genus name to 1788.
- Merriam-Webster: eu-
The prefix can express well.
- Merriam-Webster: apocalypse
The same covering verb underlies the uncovering formation.
- Online Etymology Dictionary: eu-
Also built on Greek *eu-* "well": euphoria, euphemism, eulogy
- Online Etymology Dictionary · eucalyptus
Meanings of the older forms on the word path.