Your employer is incorrect. All monies paid to an employee must be included on the W-2 and are subject to both the employee share and employer share of social security and medicare tax (7.65% each).
Ask the employer for a corrected W-2. If they won't do this, in Turbotax when entering the 1099 there is a page of special circumstances and one of the boxes you can check is "this is from my employer and should have been on my W-2". Turbotax will prepare the required extra form to charge you 7.65% employment tax instead if 15% SE tax.
By using the 1099, and possibly by changing the name, the employer is trying to avoid certain costs (social security and medicare tax, unemployment taxes and workers comp insurance, and other costs that might be based on total wages.) Possibly on purpose? Possibly simple ignorance. If on purpose, be on the lookout for other shady practices you might want to disassociate yourself from.
