Legal Question in Real Estate Law in California

It sounds like you mean that you have not received title, either through probate or a trustee's distribution, or recording an affidavit of death. Changing your own name has nothing to do with title, or taxes.

There are exemptions from an increase in property tax after a title change. When the deed is recorded changing title into your name, if an exemption applies, that is filed at the same time with the assessor's office.

If this would be considered a parent to child transfer (assuming you inherited the house from a parent) then there is an exemption of re-assessment for that.

There are no taxes on inheriting a house. You should identify the basis in your hands for tax purposes so that if you sell the house you know what the gain on sale will be.

You probably should retain an attorney familiar with estate planning, probate, real property, and property taxes and income taxes to assist you at this time.