"Whoever, having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, transmits or causes to be transmitted by means of wire, radio, or television communication in interstate or foreign commerce, any writings, signs, signals, pictures, or sounds for the purpose of executing such scheme or artifice, shall be fined under this title or imprisoned not more than 20 years, or both. If the violation occurs in relation to, or involving any benefit authorized, transported, transmitted, transferred, disbursed, or paid in connection with, a presidentially declared major disaster or emergency (as those terms are defined in section 102 of the Robert T. Stafford Disaster Relief and Emergency Assistance Act ( 42 U.S.C. 5122 )), or affects a financial institution, such person shall be fined not more than $1,000,000 or imprisoned not more than 30 years, or both."

So if you are doing things purely for anonymity it's OK, but if you are registering many email addresses to overcome email service's per account free storage limit, or if you order sex toy delivery for new identity to get a first buyer's discount multiple times, then as I understand that could be a wire fraud.