'ashcan' is a compound formed from 'ash' + 'can' in modern English (recorded from the late 19th century), literally meaning a 'can for ash'.

'ash' comes from Old English 'æsc' meaning 'ash (tree) or ash (residue of burning)', and 'can' (as a container) comes via Middle English 'canne' / 'cane' from Old North French/Medieval Latin roots meaning a vessel; the compound 'ashcan' developed in American English in the 1800s to name a simple metal receptacle for ashes and small refuse.

Initially it referred specifically to a receptacle for ashes from stoves and fires; over time it broadened to mean a general trash receptacle and later took on figurative meanings ('to ashcan' = to discard/shelve) and specialized senses (e.g., 'ashcan edition' for a low-run promotional printing).