We can’t really tell you anything about the Texas laws regarding business registration. This is an income tax form.
As an income tax matter, if you live and physically work in the state of Texas, then California will not tax your income. And since Texas does not have a state income tax, then you only have to worry about paying federal taxes on your income.
There are five or seven states that may try to tax you if your employer is based in their state and you are telecommuting from another state, but California is not one of them.
