I've noticed that recently (starting a few months ago) some of my contacts started being displayed as "Jane personal" instead of her actual name like "Jane Doe" in emails.
I find this format strange, but I can't figure out any way to get it to return to the old way. In addition this appears to only have happened to one of my contacts, but her name appears correctly in Google contacts.
Other people who she emails has mentioned seeing the same behavior–so it could be related to her Gmail account in some way.
Another interesting tidbit that I just noticed is that this doesn't occur 100% of the time. Some emails still have the name displayed in the "Jane Doe" format.
Best Answer
You can only fix this by having the sender change the settings on their iPhone.
Using the steps below they can modify the name that is displayed to others:
Settings > Mail, Contacts, Calendars
Then select the account you would like to change. (Gmail, iMail, etc.)
On the next screen, click the email address associated with that account.
The new screen has an option to change the account "Name" to your choosing. It can be anything you like whether that be "Jane," "Jane Doe," or "Awesome Girl"--it is up to you.