iExplorer determines the device owner’s name above your sent bubbles by the “Me” card on your device, so you might have the “Me” card on your iPhone set to a different contact. You can change the “Me” card on your device by tapping Settings > Mail, Contacts, Calendars > My Info (in the Contacts section).
If someone else’s contact was somehow set as your “Me” contact, just change it to your contact card, and then refresh in iExplorer by right-clicking on Backup in the left panel and choose to Refresh (PC) or Back Up Now (Mac).
If that doesn’t fix it to show your name instead, it may be due to an iOS bug which causes more than one Me card to be set. To see if this is happening on your device, please try opening the Contacts app on your iPhone and check whether you see a “Me” to the right of your name in your list of contacts and also scroll through the full list of contacts to see if you see “Me” labeled on any other contacts, especially the person whom you say is showing up next to the sent text bubbles. If you do see any other contacts set to Me, please try deleting your contact or that contact and recreate it. Then, try setting the My Info (Me) card in Settings > Mail, Contacts, Calendars.
If you don’t see any other contacts set to “Me”, please try switching the My Info field to a different contact in Settings, then switch it back to your contact, and then try refreshing the backup in iExplorer (right-click on Backup in the left panel and choose to Refresh (PC) or Back Up Now (Mac)).