Is there a Google Sheets formula to put the name of the sheet into a cell?

Question

The following illustration should help:

Answer 1

I got this to finally work in a semi-automatic fashion without the use of scripts... but it does take up 3 cells to pull it off. Borrowing from a bit from previous answers, I start with a cell that has nothing more than =NOW() it in to show the time. For example, we'll put this into cell A1...

=NOW()

This function updates automatically every minute. In the next cell, put a pointer formula using the sheets own name to point to the previous cell. For example, we'll put this in A2...

='Sheet Name'!A1

Cell formatting aside, cell A1 and A2 should at this point display the same content... namely the current time.

And, the last cell is the part I'm borrowing from previous solutions using a regex expression to pull the fomula from the second cell and then strip out the name of the sheet from said formula. For example, we'll put this into cell A3...

=REGEXREPLACE(FORMULATEXT(A2),"='?([^']+)'?!.*","$1")

At this point, the resultant value displayed in A3 should be the name of the sheet.

From my experience, as soon as the name of the sheet is changed, the formula in A2 is immediately updated. However that's not enough to trigger A3 to update. But, every minute when cell A1 recalculates the time, the result of the formula in cell A2 is subsequently updated and then that in turn triggers A3 to update with the new sheet name. It's not a compact solution... but it does seem to work.