Can you explain what you mean by somebody elses name at the iTunes store?
Is this phone new or did you purchase it from ebay or a friend?
Can you also tell us what version of iTune syou use and do you have your iTunes library backed up for your iPhone?
Is your iPhone activated?
Can you make calls?
If we have to reset the phone do you have your songs all saved on your computer?
Could you connect your iPhone or iPod touch to your computer then select your iPhone when it appears in iTunes, under Devices select the Summary tab and then select the Restore option.
Follow the prompts to complete the restore and when it is finished you will need to resetup your phone to use your account.
Let me know if you need more info.