Yes, it is considered income and is subject to federal/state taxes as well as social security and medicare taxes.
Your employer should report it on your W-2, and take taxes out of it like your regular pay. By giving you a personal check, they are transferring the extra Social Security and Medicare taxes they would normally pay to you (which you will have to pay when you claim it on your income tax return).
As far as reporting it, I would select that your business name/address is the same as your name/address, that you do not need an EIN and that you do not need to issue any 1099s when you walk through the Business Income and Expenses section.
