What is the job title for someone who has creative digital ideas for businesses?

Generally I think this kind of person is a Online Marketer, E-commerce Executive, E-commerce Manager, Digital Marketer, Either Social Media Developer/Executive....

Director/Manager Business Development.
It is responsibility of this person to explore all avenues available to develop new ideas that will help in expansion of the business, including, but not limited to online business opportunities, social media, Internet marketing, and much more.
Thank you.

This is the job of a Creative Director 

I would call the person a Digital Creative Director. The general job titles of people working in digital marketing industry are digital marketing director, digital marketing manager, digital marketing analyst, digital marketing executive, digital marketing account manager, digital marketing strategist etc.

Look up the job descriptions of various job titles and choose the title that best fits your work.