Worked for a company which ran into an S3 bucket naming collision when working with a client - turns out that both sides decided hyphenated-company-name was a good S3 bucket name (my company lost that race obviously).
One of those little informative pieces where everytime I do AWS now all the bucket names are usually named <project>-<deterministic hash from a seed value>.
If it's really meant to be private then you encrypt the project-name too and provide a script to list buckets with "friendly" names.
There's always a weird tradeoff with hosted services where technically the perfect thing (totally random identifiers) is too likely to mostly be an operational burden compared to the imperfect thing (descriptive names).
One of those little informative pieces where everytime I do AWS now all the bucket names are usually named <project>-<deterministic hash from a seed value>.
If it's really meant to be private then you encrypt the project-name too and provide a script to list buckets with "friendly" names.
There's always a weird tradeoff with hosted services where technically the perfect thing (totally random identifiers) is too likely to mostly be an operational burden compared to the imperfect thing (descriptive names).