I've read when you write your resume, it's okay to use what you feel is the most appropariate/applicable title - compared to what your actual title was if/when they are different because they often are and can change during your tenure there. You should also be writing your resumes to the jobs you're applying for. I was officially a "Data Analyst" but my role was "Webmaster" so I use "Webmaster" on my resume because that's why my role actually was and I would never apply for a role as a Data Analyst.
Developer of digital business? Sounds pretty vague. Ask them for the job description. If it's a small company, it might not yet be written and/or the role might not yet be fully defined.
If this IS your contract, I'd tell them that it's not what you agreed to and move on (unless you do agree to what they have changed on you). If it was me, I'd see the red flag, thank them for their time, and move on. Because if this is how the relationship is starting, I would bet you a donot where it's headed