Name incorrect in H1B Petition Filed


I have recently done my employer change and my new H1-B petition extension is approved by USCIS . On seeing the courtsey receipt from USCIS, I see that my name is mentioned wrongly. The law firm has filed with wrong name but all my supported documents have the correct name in it.
Please let me know the process to correct it . Will this be a process for my future visa interviews and Green card processing. Thanks as always !

correct :
First Name : A B
Last Name : C

Mistake :
First Name :A
Middle Name : B
Last Name : C

You need to talk to your attorney as they represented your case. They can open a service request with USCIS and get it corrected. USCIS will send you the updated approval notice.