1. Valid Visa Stamp: A student can re-enter using the old visa stamp that has the old school's name on it as long as the visa stamp is not expired and the student has a new I-20 and other supporting documentation. It is always a good idea to take financial support evidence with as well when presenting yourself at a port of entry.
2. Expired Visa Stamp: If however the visa stamp itself has expired then, as with all visa categories, the student will need to get a valid visa stamp allowing entry. This stamp will then have the new schools name on it. Have the student take the new I-20, financial support evidence, and the other documents required by the particular consulate/embassy to get the new visa stamp from consulate.
The only exception to having to present a valid visa stamp for students is if travel will be to a neighboring U.S. country like Canada or Mexico.