Section 34A. Whoever knowingly and willfully furnishes a false name or Social Security number to a law enforcement officer or law enforcement official following an arrest shall be punished by a fine of not more than $1,000 or by imprisonment in a house of correction for not more than one year or by both such fine and imprisonment. Such sentence shall run from and after any sentence imposed as a result of the underlying offense. The court may order that restitution be paid to persons whose identity has been assumed and who have suffered monetary losses as a result of a violation of this section.