if i were you, i wouldnt change my name. i didnt. too much headache to change all SSN, credit card, checking account, since i already have it before AOS.
the only time i advise people to add married name when they only have literally 1 full name without surname which is common in my country. i have few acquaintance with only 1 name example : GAGA written in their passport. it's so hard in the US even to buy flight ticket because it's very uncommon in US, in their visa it become Gaga FNU ( first name unknown), or in the state ID become Gaga No name GIven. such a headache. i helped them filing AOS and i just added their husband name in all forms. voila they are become GAGA IHAVELASTNAMENOW. so in my practical mind, that's when adding spouse last name make sense.