You can search for these pieces of software on Google, and many of them are known as ‘key loggers’. Perform a Google search and you’ll no doubt be pleased at the thousand of results that you will see.
Another basic way of finding out whether or not your partner has a secret email account is by searching through the history of your browser. Your Internet browser keeps a history automatically of what has been viewed, and if you have any idea that your partner is snooping around and has a secret email address, then searching through the history will tell you whether or not they have been doing things you don’t want them to see.
What’s stopping you from asking your partner too, though? Accusing a partner of having a secret email address is a rather specific accusation, and hence, you should be able to talk to your partner about the worries you are having. If you have any evidence, talk to them and tell them why you believe they may have a secret email address. This way you can talk about things and have a more trusting relationship.