In higer study which title will be legal( Maiden name ) or Changed name As per my Husband ' surname

I am a 41 year old married woman . I am from west West Bengal state and my schooling was done in west Bengal .After marriage I relocated to Mumbai. Before marriage my full name was soma Pal. After marriage , I have changed my surname to Chakrabarti as per my husband's surname. My marriage is registered according to HINDU marriage act. In my marriage certificate my name is mentioned as "Soma Chakrabarti" PAN card ,Aadhaar card , Passport are in my name as Soma Chakrabarti . and in my voter card soma Pal But all my academic documents (Before marriage ) has my maiden name but after marriage i did MBA ( with my same maiden name ). Recently I would like to go forward higher study ( That time there is no Aadhaar card system). I an working college with my new name ( Soma Chakrabarti) Now, I want to pursue higher study and I seek legal advice for the followings. 1) If I want to pursue higher study what is correct way to write my name - The changed name (Soma Chakrabarti) OR maiden name (Soma Pal) as per the previous academic record? 2)Is marriage certificate sufficient to legalize and recognize the change of my surname (due to marriage) ? 4) For Higher study If I want to go abroad with my new name( as my Passport, PAN Card , Aadhar card in Soma Chakrabarti ) ,but with academic certificates with previous surname( Soma Pal ) , will it create any problem?