This is currently untested but the U.S. Supreme Court did leave the door open to allow someone to plead the 5th amendment in order to hide their identity.
In Hiibel v. Nevada the U.S. Supreme Court held that the petitioner did not have a 5th amendment right to withhold his name from a questioning police officer.
The Supreme Court held that Mr. Hiibel could be arrested for failing to identify himself because Nevada's statute requiring identification was narrowly tailored and was not vague. The police officer who stopped Mr. Hiibel had reasonable suspicion that a crime had occurred and Mr. Hiibel could have satisfied Nevada's statute by simply stating his name; there was no requirement to turn over any papers or other documentation.
The final paragraph of the opinion speaks of the importance of the narrow scope of the disclosure requirement and then goes on and states:
...Answering a request to disclose a name is likely to be so insignificant in the scheme of things as to be incriminating only in unusual circumstances...Even witnesses who plan to invoke the Fifth Amendment privilege answer when their names are called to take the stand. Still, a case may arise where there is a substantial allegation that furnishing identity at the time of a stop would have given the police a link in the chain of evidence needed to convict the individual of a separate offense. In that case, the court can then consider whether the privilege applies, and, if the Fifth Amendment has been violated, what remedy must follow. We do not resolve those questions here.
While the court is leaving unanswered the question of whether there are circumstances where one may refuse to identify themselves, they are making it quite clear that such a situation would be very different than the case decided in Hiibel. There is a strong hint that they would uphold Fifth Amendment privilege in the situation you posit.