Dear Sir
Hope you are doing well !!
No, it is not mandatory to register the Partnership firm. But If partnership firm not registered it will lead to the following consequences:
a) It will not be possible to sue one partner against another partner or against the firm and vice versa in the court of law to claim right.
b) Partnership firm cannot sue third party in the court of law for enforcement of its right (See Sec.69 of Partnership Act 1932).
Etc.