In my view, there are two aspects - your education and your job history.
Because your degree is in computer science, I would tend toward "computer scientist". My degree is in software engineering, so I refer to myself as a "software engineer". If your degree was in information technology, you would be an "information technologist". There really aren't any rules on what you call yourself, but you do need to be careful about referring to yourself as an engineer in some European countries, Canada, and some states in the United States (specifically Texas and Florida, but there may be others) where you need to meet certain requirements to use that title.
Note that my resume does not contain a title for myself, outside of the job title for each position.
Typically, you also have a title at work. The people I work with that come from a software background have titles including "Program Manager", "Software Engineering Manager", "Software Engineer", "Embedded Software Engineer", and "Systems Engineer". On my resume, I include the title that I held within the organization for that position. Titles vary, but in my experiences, they are generally easy to understand, especially when coupled with a brief description of what you did and what you were responsible for.
Any CV or resume should explicitly include your educational background (including the title of the degree program) and relevant work experience (including job titles and descriptions).