Changing email address gives MSO Outlook problem

I am changing my normal email address from one I've had for many years from "mail.com" to a gmail address. I use MSO Outlook 2010 on my PC to handle my emails, both for my main email address and other, lesser used ones. Each address has a different Outlook .PST file. The main one, and the one for my current normal email address, being outlook.pst. I use POP email.

When I've changed to using my gmail address I want to keep using outlook.pst for my main email.

For, hopefully, ease of understanding, let's assume these are the email addresses:-

email-1 is my old normal address
email-2 is my new gmail address.

My plan has been to create another .pst file, email-1.pst, and setting it to handle newly received email for email-1.

Change the account details for outlook.pst to the email-2 account, both the normal details and the additional details.

This is working fine in that new email-1 emails go into the Inbox in email-1.pst, and emails sent from there are fine; new email-2 emails go into the Inbox in outlook.pst, and emails sent from that account are - almost - fine.

And there's the rub.

An email sent from email-2 goes out apparently ok, and looks ok to my son, a gmail user.

However if I send an email to myself from the email-1 account, Outlook shows in the From info

my_name <my_name@gmail.com>; on behalf of; my_name <my_name@mail.com>

Looking at the email properties I see

Sender: my_name <email-2@gmail.com>
From: my_name <my-name@mail.com>
X-Google-Original-From: "my_name" <email-2@gmail.com>
Reply-To: <email-2@gmail.com>

So despite me choosing the correct From email in the drop-down list it still uses the old email address in the From data.

Thoughts on what I've done wrong would be most welcome.

TIA

The email account associated with outlook.pst was email-1@mail.com. What I'd done was to change the email account associated with outlook.pst to email-2@gmail.com.

What your reply prompted me to do was to change the default email account to email-2@gmail.com. I've now done this.

Sadly, despite restarting Outlook, it doesn't appear to have made any difference :-(

It's definitely a POP account. I've attached 2 anonymised capturesm which I hope will help explain.

outlook.jpg shows Outlook's account choice dialog. This shows all accounts are POP accounts. The first is highlighted and is for email-2@gmail.com, at the bottom the associated .PST file is outlook.pst.

outlook1.jpg shows the dialog when clicking edit for that first account.

Clearly it's a POP account, and uses outlook.pst.

Had a look at the Gmail webmail settings. They were the problem. Changed Gmail's default Send As address to the email_2 address and it looks to be ok now.

Thanks for your thoughts, they pointed me in the right direction - eventually!