Currently seeking to separate from my spouse. I purchased the home before we were legally married and only my name has remained on the deed.
It is yours
They can make a argument for equity or debt pay-down during the marriage which they may or may not get
Encourage them to leave, if not you need to go through the options with attorney
The house is your separate property, but your spouse is entitled to half of any marital equity built in the home during the marriage. You can certainly ask him to leave, but there is nothing you can do to evict him, so to speak, if he refuses.