Traditionally if you wrote a letter on someone's behalf (eg they instruct you by phone on what to say and to get it in the mail as fast as possible), you sign is 'PP J. Smith'. PP is short for 'per procurationem' meaning 'by the agency of'. You don't need to know Latin, just that 'PP [name]' means it was sent on someone's behalf.

If I got a letter with no indicator and it turned out to be someone's secretary I wouldn't be offended exactly but it would make me a little wary until I was more familiar with the person and their working habits, eg maybe they have total trust in their secretary, but the secretary isn't familiar with this convention.

Obviously I'm a bit old-fashioned about these things, bt these conventions came into being for good reason.