It should be so easy but I couldn’t find any methods to define a different name for the developer field for an app store app.
For example: Most of the Electronic Arts games have different company and developer names. Command & Conquer Red Alert game belongs to Electronic Arts company but it is developed by EA Swiss Sarl company.
How can I achieve this?

The first time you submit an application, Apple will ask you to choose the company name as it will appear in iTunes.
But be aware that it cannot be changed afterwards:
Everything is explained in details in the iTunesConnect Developer Guide (PDF)
EDIT
The terms are very confusing. I got confused myself. The Company Name mentioned in my answer would be “Electronic Arts”. I realized you are talking about the real company name (EA Swiss SARL), it’s the legal name of your company, listed in your “Organization Profile” in Apple Member Center. I checked my account, and it cannot be change. I believe you can contact Apple Dev support at devprograms@apple.com and ask them to change your legal name. But they will probably require legal documents to do so.