Should I update to USCIS with new Passport info

[Thuy]

I am green card holder. My passport expired in the beginning of this month and I applied for and received the new one. The new passport has a different passport number to my previous one, although all the other information is the same and The name is still in my maiden name but on GC is changed into married name.

My question is that I do need to update my information and how I do that?

Thanks in advance.