After you log in to gmail, click the gear icon then click settings. Now, from there I'm not sure which tab will address your issue. I suspect "accounts and import" then "sent mail as".
on your mac, when u send an email to yourself, let its say (Holidays in united states). hover your mouse over that blue bubble containing that text until you see the drop down menu. choose "Remove from previous recipients list" should be gone!!
on your mac, when u send an email to yourself, let its say (Holidays in united states). hover your mouse over that blue bubble containing that text until you see the drop down menu. choose "Remove from previous recipients list" should be gone!!