You would still have the same age, gender, personality, skin color, etc. and you would be able to speak at least one local language and would know basic information of the era and place. Your family, social standing, and such would be randomly picked.
1600 India. I’m royalty and get to meet my ancestor and favorite historical figure Akbar. And yes the mughal empire is my roman empire
Social standing is random though based on OP’s rules. It would be terrible to end up as part of the lowest caste.
I think the only caste Mughals did was your clan.