Name change while H1-B approved

[LincolnMateo]

Hi,

My previous passport had my whole name in the first name field and nothing in the last name. I got my H1-B approved on my previous passport. My SSN is also based on the previous passport only https://trackeasy.fun/usps/ https://showbox.tools/ .

Now I need to update the name on my SSN. Can anyone tell me what's the way forward to change name in SSN? Do I need to file H1-B amendment as well? What about name update in I-94? I am not planing to exit the US anytime soon because of the pandemic.

Thank you.