Get an alias address in the sender's field in Gmail

Let's say I have two Google accounts: perso@gmail.com Y pro@gmail.com.

I'm connected to Gmail in my perso account. I have added Pro as an alias address to send mail as, in the Gmail settings (Settings> Accounts and Import> Send mail as).

But, when I select the pro@gmail.com Address when sending an email, some of my contacts sometimes still see the original, perso@gmail.com address. And when checking the raw message, it seems, perso@gmail.com it is still used in the Sender: field; pro@gmail.com it is only present in the Since: field.

How to do it so that the people to whom I send the mail. Never see the address perso@gmail.com? I tried to mark and unmark "Treat as an alias" in the Gmail settings, but this did not change.