How to change my app’s developer name on Apple's App Store?

Solution 1:

1. Enter here: https://developer.apple.com/account/
2. Press "Membership" (on the left list, 2nd button)
3. Press "Need to edit this information?"

And choose what you need and fill the form I did before That's all :)

Solution 2:

Apple has answered this question under Account Management section. Solution still remains same as pointed by Undo.

If I am enrolled as an individual, can I change to a company membership?

Yes. To convert your iOS Developer Program membership from an individual to a company, please contact us. You can make this change only if you are the founder/co-founder of the company. As part of the conversion process, you may be asked to submit business documents to verify your company's identity.