Legally you should change your documents is the general rule. Now if you don't and you have to take admission then you have to provide a affidavit providing that you are providing all the information to be correct and the certificates, documents you provide are of the same i.e., you with two names as your new name and your old name. You can visit any lawyer and he/she can draft it.

I would highly recommend you to contact the college you want to take admission in and get it discussed with the officials. They may provide you more information regarding the format of affidavit or the rules you need to abide etc.

I hope this helps. All the very best for your future endeavors!