I had my name changed (including first and middle) about three years ago. To be frank, the legal process is a hassle but if you think switching out your names will be easier for you in the long run and you think it is the best choice for you, then by all means, do it.
First, yes, you can legally change your name. Different states have different procedures but the general protocol is to file a petition with your city's Superior Court. Additional paperwork include background checks, a statement detailing the reason why you want this change and what you want to change it to, and a request for any widely-circulated newspaper within your state to publish a public announcement of your name change.
That last part is a requirement so that the state doesn't think you're changing your name to run away and conceal your identity from the police if you have an outstanding warrant or creditors/ lenders whom you owe money to.
If your university has a student legal services department, I highly recommend you have someone there to help you file and arrange the paperwork properly. It will save you a lot of grief.
Second, once your petition and paperwork have been filed and submitted, you may or may not (depending on which state you live in) have to pay processing fees for your newspaper publication AND to the court. A clerk will then give you a court date for you to appear so a judge can review and grant your petition. Since most name petitions are granted, it is highly unlikely you will be required to directly speak to the judge unless he/she has a concern they wish to discuss with you.
Third, when your petition has been granted, you must obtain certified copies of your granted petition. That document is proof that your new name is valid so hold on to it carefully. You will then need to notify many institutions of your name change. These include:
Social Security
DMV
Passport Services
IRS
Any Lenders and Creditors you've had transactions and/or hold accounts with
Any Banks you've had transactions and/or hold accounts with
College/Universities you have attended or will be attending
Department of Vital Records (for birth certificates)
U.S. Post Office
U.S. Registrar of Voters
Former and Current Employers
Hospitals/Pharmacy (for medical records)
etc. etc. etc.
The entire process can be from anywhere to 6 months up to 1 year.
To get more concrete information, you could browse through your state's court website and see what the protocol is for a name change in your state.
Sorry for the wall of text but I hope this helps. Good luck!