Relevant law for awareness:

Illinois Ill. Comp. Stat., ch. 725, §5/107-14 ( https://www.ilga.gov/Documents/legislation/ilcs/documents/072500050K107-14.htm )

(a) A peace officer, after having identified himself as a peace officer, may stop any person in a public place for a reasonable period of time when the officer reasonably infers from the circumstances that the person is committing, is about to commit or has committed an offense as defined in Section 102-15 of this Code, and may demand the name and address of the person and an explanation of his actions. Such detention and temporary questioning will be conducted in the vicinity of where the person was stopped.

I’m not sure what the specific definition of a “peace officer” is in this context, but because this is Illinois state law it probably only applies to Illinois state officers and not federal officers. Also:

[…] since the Illinois Second District Appellate Court Decision in People v. Fernandez, 2011 IL App (2d) 100473, which specifically states that section 107-14 is found in the Code of Criminal Procedure of 1963, not the Criminal Code of 1961, and governs only the conduct of police officers.

Assuming this interpretation from Wikipedia is correct, the above only applies to police officers. Also an interesting nuance:

[…] in Illinois, officers “may demand” a person to identify themselves, but a refusal to do so amounts to mere argument with police, which is protected under the 1st Amendment. As such, refusing to identify yourself in Illinois is not obstructing identification or obstructing justice.

https://en.wikipedia.org/wiki/Stop_and_identify_statutes

In the present situation, I recommend everyone become familiar with their local jurisdiction’s stop and identify requirements.

Loser: “I AM an officer!”

Same loser: “OK. Call 911.”