Problems with sender when using two gmail accounts.

I have two gmail accounts, one personal, one professional. My problem is that when I send a message from my personal account, or when I reply to some message received in this same account, the person to whom I send this e-mail receives it has if it was sent from my professional account. This happens even when I correctly set the sender field.

Did anyone had the same problem? Can you help me.

Thank you in advance,

J.