You can move your logins to another keychain in both your browser extension your mobile app.
When you first create a new login, you can also choose which keychain you want to store this login in, thereby separating your private and business logins.
If you have saved a login in your private keychain and want to move it to your company's keychain, you do this by accessing your passwords in either the browser extension or your mobile app, tapping that login. Then edit and change the account type to the keychain you want.