I apologize for my delay responding, I've been hospitalized.
Here's what Patrick wrote, "First, BBEdit will automatically increment
each new document's (ID) number until you quit and relaunch it, and
there's no separate option for doing so.
Next, BBEdit will by default always preserve unsaved changes across a
quit and relaunch, and this process will also preserve the titles of any
open, unsaved documents. If however you do not want BBEdit to preserve
unsaved changes, you can prevent this by turning OFF the option to
"Restore unsaved changes" in the Application prefs panel.
Last, I do suggest using BBEdit's global scratchpad instead of
individual unsaved documents for the sort of task you describe, and
please note that if you wish, you can assign a key shortcut to the
Scratchpad window via the Menus & Shortcuts prefs pane. (I've done this
myself and find it very handy.)"