Take away my first letter and I remain the same. Take away my last letter and I remain unchanged. Remove all my letters and I'm still me. What am I?

Why this works

This riddle plays with the different interpretations of the word "mailman." When you remove the first letter 'm', you still have "ailman," which phonetically sounds similar to "mailman," keeping the essence of the term. Similarly, removing the last letter 'n' gives you "mailma," which still conveys the idea of someone who delivers mail. The clever twist comes from the phrase “remove all my letters,” which humorously suggests that even without the letters of the word, a mailman still exists in the world, as they are not defined solely by their title but by their role in delivering mail.