In general, you will find that most major insurance companies have very strict rules about insuring rebuilt title vehicles as such vehicles open the insurance companies to potential liabilities that they do not want to have exposure to. If you are looking for a major firm that might work with a rebuilt title vehicle check with GEICO, State Farm, Progressive, or AllState. They are insurers that tend to work with higher-risk vehicles and customers because their pool of insured vehicles is among the largest on the market and they can take on these riskier vehicles, while others may not. In all this, the bottom line is check with your insurer.
For more info, see Things to Know About a Rebuilt Car Title