That won’t happen, unfortunately. Jamal Khashoggi Way" is a “symbolic name”, not an “official name”. The embassy’s address will not change.
The committee report (PDF) describes the legal status:
The Street and Alley Closing and Acquisition Procedures Act of 1982, effective March 10, 1983 (D.C. Law 4-201; D.C. Official Code § 9-204.01 et seq.) (“Act”) establishes procedures for closing streets and alleys, opening new streets and alleys, naming public spaces, and other procedures related to streets and alleys. The Act authorizes the Council to symbolically or officially designate or change the name of any public space in the District of Columbia, including streets and alleys.1
In October 2016, the Act was amended to create a clear distinction between official and symbolic street and alley namings and to establish distinct processes and requirements for each type of naming.2
An “official name” refers to the legal designation of an alley or a street for mailing address and other purposes,3 whereas a “symbolic name” for a street or alley shall be in addition to and subordinate to any name that is an official name.4
An official name of an alley shall contain the suffix “Alley” or “Court.”5
A symbolic name of a street or alley shall contain the suffix “Way” or “Plaza.”6
As established by Bill 24-22, “Jamal Khashoggi Way” is a symbolic street designation for New Hampshire Avenue N.W., between Virginia Avenue N.W. and F Street, N.W.