You can try to out only one last name, but they will more than likely add your second last name when you go to apply since it has to be like its shown on the EAD. Legal alien allowed to work.
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Self filed AOS │Apps Received By USCIS - 3/18/19
│Biometrics Done - 4/11/19
Interview Scheduled - 4/24/19│Interview Date - 5/31/19│AOS Approval - 5/31/19
Permanent Resident Card Received - 6/8/19