To set up an alias to your account navigate to the account settings under Menu > Tools > Accounts, select your account, click on "Aliases" under the General setup of your account and add your email address to the list of Aliases.

Note: In order to send out on behalf of this account eM Client may require an initial setup of the account with your mail server, for example connecting the two accounts in your online Account settings. For example for google accounts you first need to go to gmail.com and in the settings link the two accounts.