Is it possible to have a pivot table automatically incorporate newly added 'Filter by' values or show the current values?

I've made a test sheet here (https://docs.google.com/spreadsheets/d/17l49Rn3ZbNx-upzBtmRtsJBHQiCKXuYPs8SMTyrcw9k/edit#gid=0)

You'll notice that the pivot table IS correctly pulling in ALL the data in A:B, not just limited to the existing rows of data.

This way, as new rows are appended, the data is automatically added to the pivot.

However, I've discovered a limitation. If a new row contains a new Name value, e.g., C, then that will NOT get automatically added to the pivot, since the pivot has a filter. Even though the filter is for "All items", since C wasn't existing at the time at which the filter was added, once I add a row C, I have to manually adjust the filter (re-select all) to pull it into the pivot.

This is not desired behavior for me, I would like the pivot to not be constrained (i.e., if it previously was set to select all, then continue selecting all) UNLESS I had said only A, then don't give me C even if C is appended!

Is this possible?

Or if not, at the very least, is it possible to print out the filter somewhere formulaically? (in a cell, =Filter(pivot)), this way at least I have a warning/reminder?

Other solutions to deal with this welcome!