How can I change my email account name to my alias?

The Verizon email address all my friends, family, and business associates have used for more than 8 years (Jxx Sxxxx) turns out to be an alias. My primary account name seems to be JSxxxx. I recently changed to high speed enhanced and these things happened:

Outlook, where I receive my email, continues to receive all mail addressed to Jxx Sxxxx, just as it always has. If I compose a new email or hit the reply button, my outgoing emails SHOULD show up in the recipient's mailbox as Jxx Sxxxxx. Instead, they appear with the sender name Mxx Sxxxx (the name of my husband, the account owner). I need my own name back in order to get my emails read by business associates and others who don't know who Mxx Sxxxx is. 

In addition, only email addressed to JSxxxx comes to my regular Verizon account (accessed at NO email addressed to Jxx Sxxxx comes to that account, which means that if I am away from my computer I cannot access my email at all.

How can I change my so-called account name to my alias without losing all the emails in my Outlook account? That is, how can I get rid of my primary account name, and substitute my alias?