You can change your name on your USCIS documents if you have State issued ID in a common law name. They made this policy update on July 12th 2024 according to a recent policy update memo.
USCIS Policy Manual Volume 1 - General Policies and Procedures provides:
Part E - Adjudications
Chapter 5 - Verification of Identifying Information
A. Full Legal Name
In general, the requestor’s full legal name is comprised of the requestor’s:
Given name (first name);
Middle name(s) (if any); and
Family name (last name).
The legal name is one of the following:
The requestor’s name following a common law name change evidenced by a state-issued identification document.[2]
1. Name Changes
The place of jurisdiction controls whether the name change is legally valid.
Common Law
In the United States, including its territories and possessions, state and local law govern name changes. Therefore, USCIS may issue a document in a new name based on the operation of the provisions of any state or local law that recognizes a new name. If the requestor resides in a state that recognizes common law name changes, the requestor may provide a state-issued identification document and appropriate documentation issued by the state or locality recognizing a common law name change based upon customary usage. The documentary evidence should show the issue date, acquired name, and at least one other piece of identifying data such as the applicant’s date of birth, place of birth, age, photograph, or Social Security number. Acceptable documentary evidence includes but is not limited to driver’s licenses and non-driver state-issued identification. For questions relating to the validity of a common law name change, officers may review the case with local counsel.
Footnotes
[^ 2] Certain states recognize common law name changes. USCIS recognizes common law name changes if the benefit requestor’s state of residence has recognized such a name change through the issuance of a state-issued identification document. See Subsection 1, Name Changes [1 USCIS-PM E.5(A)(1)].
[^ 5] In the United States, including its territories and possessions, state and local law govern name changes. Therefore, USCIS may issue a document in a new name based on the operation of the provisions of any state law that recognizes a new name. If the requestor resides in a state that recognizes common law name changes, the requestor may provide a state-issued identification document recognizing a common law name change based upon customary usage. The documentary evidence should show the issue date, acquired name, and one other piece of identifying data such as the applicant’s date of birth, place of birth, age, photograph, or Social Security number. Acceptable documentary evidence includes but is not limited to driver’s licenses or non-driver state-issued identification. See Subsection 1, Name Changes [1 USCIS-PM E.5(A)(1)].
USCIS Policy Manual Volume 12 - Citizenship and Naturalization provides:
Part K - Certificates of Citizenship and Naturalization
Chapter 4 - Application for Replacement of Naturalization/Citizenship Document

B. Requests to Change Name or Date of Birth
1. Certificates of Naturalization
Applicants may submit Form N-565 to update their name on a replacement Certificate of Naturalization based on a name change ordered by a state court with jurisdiction, or by operation of law, including a common law name change evidenced by a state-issued identification document, or a name change resulting from marriage or divorce.[7]
Footnotes
[^ 3] Certain states recognize common law name changes. See Volume 1, Policies and Procedures, Part E, Adjudications, Chapter 5, Verification of Identifying Information, Section A, Full Legal Name [1 USCIS-PM E.5(A)].
[^ 4] Certain states recognize common law name changes. See Volume 1, Policies and Procedures, Part E, Adjudications, Chapter 5, Verification of Identifying Information, Section A, Full Legal Name [1 USCIS-PM E.5(A)].
[^ 7] See INA 343(c). See Volume 1, General Policies and Procedures, Part E, Adjudications, Chapter 5, Verification of Identifying Information, Section A, Full Legal Name [1 USCIS-PM E.5(A)].