Hello student,

Don't panic. Even if your aadhaar card doesnt have you full name, you are allowed to appear for MHTCET. Aadhaar card is only checked during entering the center just to confirm the identity of the person. So, if the aadhaar card contains a valid photo of yours, then you are eligible to appear. Moreover, you may also bring any other validation certification such as drivers licence or passport to confirm your identity.

I hope this helps, All the Best!