Hi ilonakarow,
If this is happening with just one email account, your name mail be incorrectly set up for that account.
You can check on your iPhone under Settings > Mail > Accounts > Name of Account > Account. If the name is blank or incorrect there, you can edit it and then hit "Done."
We also recommend restarting your device and keeping it updated as those steps assure you have cleared out any minor software issues and are running the most current version.
Restart your iPhone - Apple Support
Update your iPhone or iPad - Apple Support
If you still see the issue, let us know and we will take it from there.
Cheers!