The answer to this depends on whether your F-1 student visa stamp in your passport is still valid or not. Note that this only becomes an issue if you as the student decide to leave the U.S. and you then seek to re-enter.
If you have already been admitted to the U.S. then your I-94 controls how long you can stay in the U.S., and for students it normally states D/S for duration of stay. However, if you transfer schools and you are going to travel, then read the following sections to determine if you need to go to the U.S. consulate/embassy in your home country before attempting to re-enter.
Do I Need to Go to the U.S. Consulate Before Re-Entering the U.S.?
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 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.