How To Get Rid Of On Behalf Of When Sending Emails Through A Second Gmail Account

I read my personal email and job search email on my one personal single email inbox and when responding to job search emails I pick the job search email address from the “From email” drop down list on compose email

The issue is the recipient sees both my email address as “personal email” on behalf of “job search email” which defeats the purpose of hiding my personal email.

I tried “don’t treat as alias” etc while adding the email account but does not help

Any suggestions?