Changing or Removing Developer Name in App Store

I have created an application for my customer. We have published the application with my account. Now, they want to change the developer name as their company's name. Is there a way to change the developer name? Can I move my application to their business account so that Developer name changes to their business name?

Yes, you can transfer the app to other since WWDC 2013. Also, you can call the Apple Support to change the Seller Name. Here is a video about this: App Transfer Tutorial.

My apps initially appeared in the App Store with the wrong seller name. I don't personally own a credit card, so a family member who did paid my developer subscription. While my correct name appeared elsewhere, under Seller it showed the name from the credit card. I used one of the contact options in iTunes Connect to request a name change, which was applied within a few days.

On the current Contact page, the Contracts and Legal category includes Request Name/Address update. Try that.

You'll certainly find it easier to rename your account than to move the app to a different account. Here's what they say about that.

I sold my app to another developer and can no longer distribute it on the App Store. Can I transfer the app to the new developer's iTunes Connect account?

No, you can’t transfer the app to another developer account on iTunes Connect. To add the app to another account, remove the app from the current account and upload it to the new iTunes Connect account.

Note that uploading the app to a new iTunes Connect account will disable current customers from receiving automatic and free updates of your application. All customer reviews, rating, and ranking information will be reset. You will not be able to reuse the app name and SKU in the old account. If you have uploaded a binary or used the app with the iAd Network, your Bundle ID will not be reusable either.

This is only applicable for the part of the OP's question:

Is there a way to change the developer name?

The most simple way I found to CHANGE the developer name was by filling out a request on this page:

Contact Us Page

Then select from the option:

Enrollment, Membership, and Account -> Account Updates and Renewals

I just told them which names I would like to user, First name and surnaame.