If prenup is signed and husband purchased a property without wife name on it, is it considered marital property?

So it depends on how you did the prenup.

Like the way that I usually recommend to do the prenup is if whatever you buy in your name is yours, whatever wife buys in her name is hers.

Then in this situation, it would not be considered marital property.

Because you decided at the beginning of your marriage that anything I buy in my name is mine.

Whatever you buy in your name is yours.

However, if you didn't have a prenup, then yeah, obviously that would be considered marital property.

So it depends on what type of terms you use in your prenup.