Unless the entity purchasing the home is, itself, a legal entity such as a C, S or LLC corporation (an LLC is, in fact, a corporation--limited liability corporation), you will be unable to purchase a home in your name using just your Federal EIN. Keep in mind that most EINs or Employment Identification Numbers are "tied" to someone's actual social security number, so if you offer an EIN as the identity of the purchaser, the information will be run, first, for the corporation and if there is none, then for the individual with whom the EIN is tied. If you are not the same person whose SSN is attached to the EIN, it would definitely raise a red flag for any bank.
If you wish to purchase the home for yourself, rather than as the asset of a corporation, it's best to use your own social security number in buying the property.
Grace Morioka, SRES, e-Pro
Area Pro Realty