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

Question

The following illustration should help:

Answer 1

if you want to use build-in functions:

=REGEXEXTRACT(cell("address";'Sheet1'!A1);"^'(.*)'!\$A\$1$")

Explanation: cell("address";'Sheet1'!A1) gives you the address of the sheet, output is 'Sheet1'!$A$1. Now we need to extract the actual sheet name from this output. I'm using REGEXEXTRACT to match it by regex ^'(.*)'!\$A\$1$, but you can either use more/less specific regex or use functions like SUBSTITUTE or REPLACE