Another question: how were jobs assigned to people?
Adding to the question, could you make your own job?
In general, Soviet citizens had the right to leave their job and find another. The exceptions were:
People in colony-settlements (kinda like a prison just without guards, walls and regime but you still not have a right to leave anyway). But it is mostly becasue they usually didn't have much variety in available work around, so changing jobs was a problem for them.
People who were given their job by a court decision as a part of their punishment aka public works. So they had to work in this particular job until the end of their sentence.
People who finished their higher (university) education were assigned to a specific positions by a state and had to work there for a set period of time. For example, if you completed an university course and became qualified teacher, then the state will give you a choice between several possible assignments in the schools around the country and you had to choose one of them and work there for a several years.
If your example do not fit in either of this three categories (you aren't in a settlement colony as a punishement, you isn't a criminal who was given public works punishement and there is obviously no higher education involved in a working as garbageman) then you are free to leave your current job and apply for some other either by looking for it on your own or by going to the local labor exchange and asking for vacancies available to your skillset and education.