This answer is based on my experience of the current market. A Phd. from a top branded institute is good, but you’ll have to market yourself.
The employers search for candidates who have clear goals. They will try to figure out why you choose a certain subject and college and your past achievements, among other things.
Try to have a look at the placement figures of IIT Tirupati for Phd., and consult the faculty members in this regard.
Brand name has its own value, but you must have a good grasp on your subject to clear interviews. This applies to any branch or college student.