I tend to go by Binary Large OBject (BLOB) storage to discern between this kind of object storage and “object” as in OOP. BLOB is also what databases call files stored in columns.
Google buckets is a bit off - the product is called Google storage. Buckets are also a term used by s3 and are equivalent to azure blob storage containers. They are an intermediary layer that determines attributes for the objects stored within it such as ACLs and storage class (and therefore cost and performance).
As to your question, object storage[1] seems to be the generic term for the technology. Internally they all rely on naming files based on the hash of their contents for quick lookup, deduplication, and avoiding name clashes.
"blob storage" is the usual generic term, even though Azure uses it explicitly. It's like calling adhesive bandages, "bandaids" even though that is a specific company's term.
AWS is S3, google is buckets, Azure is blob storage, the open source version is … ?