Entry revised for OED Online

  identity theft, the dishonest acquisition of personal information in order to perpetrate fraud, typically by obtaining credit, loans, etc., in someone else's name.

1989 Sun-Sentinel (Fort Lauderdale, Florida) 6 July (Nexis) (headline) *Identity theft besmirches victims' records.

2003 R. WHITNEY Millionaire Real Estate Mentor xv. 244 If you are a victim of identity theft, prompt action makes recovering somewhat easierbut be prepared for a frustrating, lengthy process.