If you are Married Filing Separately, IRS regulations require that your spouse's name and Social Security number must appear on your return. This serves two purposes. First, if there are items of joint income or deductions, or joint estimated tax payments, it assists the IRS in reconciling the separately reported allocations of these amounts.
Secondly, there are regulations that provide for coordination between the tax returns of spouses who file separately, most notably, the requirement that both spouses must treat deductions in the same manner -- either both must itemize deductions or both must take the standard deduction. Having the spouse identified on each return allows better coordination between the two returns.