Can a married woman buy a house without having her husband's name on it?

First there is a general rule that says that assets purchased during a marriage are assumed to be marital assets. That is because generallymarital funds are used (money earned during a marriage is marital money). Now, that is a presumption that can be rebutted. Say that the woman purchased the house with funds that she inherited that has never been co-mingled. Then the house would not be purchased with marital funds.  Or money saved prior to marriage that was never co-mingeld. Or sale of stock that was kept separate. So the particular facts matter here.  Good luck.