Sending emails from multiple email addresses via one SMTP server

I want to send emails from multiple email addresses like test@test1.com, sample@sample2.com via one smtp server that is against one email address. But when I do this I get following error:

raise SMTPAuthenticationError(code, resp) smtplib.SMTPAuthenticationError: (535, b'5.7.8 Username and Password not accepted. Learn more at\n5.7.8  https://support.google.com/mail/?p=BadCredentials

My SMTP settings are:

export CR_AUTH_MAIL_SERVER=smtp.gmail.comexport CR_AUTH_MAIL_PORT=587export CR_AUTH_MAIL_USERNAME=testing@stackoverflowQuestion.comexport CR_AUTH_MAIL_PASSWORD=sampleForQuestion

If I use email address other than testing@stackoverflowQuestion.com, it is giving me error.

Can I send emails from multiple valid email addresses by using one email adresses ? I'm always receiving emails from testing@stackoverflowQuestion.com.