I still have name

my_name

, but the project name

my_project/.datasets/my_name

rather than

my_project/.datasets

Yes, this is the expected behavior

And I don't see any new projects / subprojects where that dataset creation Task is stored

They are marked "hidden" hence by default you cannot see them in the UI (so they will only appear in the Dataset page),
you can turn the UI hidden flag by going to your settings page and selecting "Configuration" then click on "Show Hidden Projects"

And also to resolve the project name depending on the version of a client

If the client is using Dataset.get(dataset_project="my_project", dataset_name="my_name") with the new clearml SDK it should work