Some, if you were the lower castes (varnas). There is a distinction between the varnas (which is more like an umbrella term for what kind of job you have) and jaati (which are endogamous groups which you can't marry outside of, usually consisting of the people of your occupation in your area). A lot of it depended on where you are, and how strictly the local attitude towards caste is. It is interesting to note that the caste system is relatively new in Indian history (dating from the Gupta period when it was really made ironclad), and that there is so little intermarriage (in some places) that the castes are becoming genetically distinct from each other due to genetic isolation. Besides that, you can tell where an Indian person is from, what their family's traditional job is, and what caste they are based on their name. So, before it became so entrenched in Indian culture that names became tied to castes, I would wager it was easier to move from one job to another.