Less derogatory term for dump

Stack Exchange notifies you: Draft Saved. I'd simply go with Drafts.

How about last session or session data?

You haven't explained whether this "name" is something that will necessarily be presented to the users, or just an internal name in the app. If the latter, who cares what it's called?

If the former, why expose some internal working of the application, you should be presenting the user with some guidance on what activity they can perform, such as:

Continue where you left off.

Or

Pick up what you were working on last time.

I suspect you are in need of user interface design (UI) assistance, not English help.

You might consider cache, as in muse cache, idea cache, session cache.

Here cache means something stored away for future use.

Another word is repository, which, in computing, is a location where data is stored and managed.

Then there is archive, which generally means a long-term or permanent storage for information.