you have to talk to your boss that report the tax under your wife's name and her SSN. then your boss will sent your wife a w-2 form, but indeed it was you work there.
another though is:
you boss want to make sure you did not report you had worked for him and do not want to pay tax. if you report, it will put your boss in hot water.
so talk to your boss to see what he really want, if he insiste to report, give him your wife's SSN, if he just want to make sure that you do not report the income. then you both OK. you boss just afraid that if you report the income, he will got fine.