Legal Name Change After Marriage

If a spouse in India changes its name after marriage, the husband keeps the name as his surname and also adopts the surname of her husband, she changed her identity completely OldFirst OldMiddle Oldlast to NewFirst Husband's_First Husband's_Last. We only have a marriage certificate that lists the names of his old and new to this subject. Although treatment of the green card in the U.S., the USCIS is asking for more evidence on the legal name change. Can you please suggest what other legal document can be provided?

SSA, the Social Security Administration, you will receive your SSN in your new name. Complete the forms using your SSN USCIS again with your new name.