L2 to H4 and change of name in SSN


I was on L2 when I came to USA two years back. I was having before marriage name on passport at that time. So I got SSN with that name.

Then my visa got changed to H4. Subsequently, I went to India and changed my name in passport to include my after marriage name (last name and middle name). and got visa stamped with new name.

I m back in USA. Now, my question is : Can I get my name changed in SSN since now I am on H4?

Thanks and regards,