Well there are many ways, most of the Hindu surnames are representatives of their castes- for example Sharma means High Caste Pundit, (Agarwal, Agerwal, Agrawala, Agarwala, Aggarwal, Agrawal)-> all mean a Bania(Trader) Caste etc etc.
You can check out a wikipedia page which can be used to map it - https://en.wikipedia.org/wiki/Category:Indian_family_names
Apart from that, you are required to submit your caste certificate in school in for Board Registration, which is loosely handled, hence process is not anonymous, so now your schoolmates know your caste.
In my College, there were many ways to know the caste of the person- like Fee structure is different for SC/STs and Others.
The whole list used to be published publicly, and everyone had to refer to it during semester registration. Now everyone who notices your name knows you an SC/ST.
There was huge resentment in the General/OBC community regarding the Fee Structure, as they just see that his mate is paying almost 1/10th the fee. I usually didn't reveal my caste to anyone, and my surname is a bit ambiguous so sometime my peers/friends used to rant about it as well.
Now after college, I have lived in around 3 major cities- Mumbai, Delhi and Bangalore. Usually no-one asks about your caste here, but it does happens sometime.
People belonging to Higher caste have no issues in revealing it, though people in my/lower communities usually hesitate and do not want to reveal it.
Moving to other city and rebranding yourself as an higher caste might work, but if caught, there can be social severe repercussion. Caste hierarchy is actually flexible and dependent on the social position of the caste in that specific area. So you would also find cases, where X is a higher than Y in some places.
Arranged Marriages in India are most mostly caste based as well.
People also associate caste with IQs as people of lower caste using reservation didn't had to score much in their entrance exams, hence usually I avoid the topic all together if possible. There are other traits as well that people assume.
Now not everyone would discriminate against you, its almost like not every white guy is racist in US, but you would very much like to just avoid interacting with the ones who are.
But I would still say an inherent Bias is still present.
In short, answer to your question- yes rebranding yourself is possible, though its not very simple. There is even a term for it in sociology named Sanskritisation. There is also Brahminisation, which is when a group adopts social traits of Brahmins who sit at the top of the caste system.