I know that in Scrum there is only three role, Product Owner, Scrum Master and Development Team. As a sign of change we must be important, not only understand these roles, but also start to change the job title to an homogenic form as Developer, Scrum Master and Product Owner. Maybe this is pointless, but we try to set an identity to the team, currently there is a mixture of titles and departments for the members of the same Development Team and we wan to change it. So how does an organization work this thing? A restructure of this is part of implement scrum or this don't care? Thanks for your advise
Roles and job titles are distinct entities. You don't need to change job titles at all, if the jobs have not changed.
For example, it's perfectly normal to have job titles of "Java Developer" or "C++ Developer". It's also normal to have pay grade and experience titles like "Senior Java Developer". This is what you do in the company.
For Scrum, no matter what title you have, both a "Junior Java Developer" and a "Senior C++ developer" are a "Developer". Their seniority has no influence on how they act on the team in regard to the Scrum process. A Senior's estimation is not worth more than a Junior's estimation. A Junior's opinion on the retrospective is not worth less than a Senior's.
So job titles can stay as they were, as long as all adhere to Scrum principles and those titles match what they actually do. Obviously if you have a PM that now is the Scrum Master, this person may want to get his title changed. But because it's a different job, not because Scrum dictates job titles.