I wouldn't assume that.Unfortunately I found that if you have an umbrella policy - your home and auto need to be with the same company.
So I found it to be an "all or nothing" - same company with home/auto/umbrella
We have our home insurance with Armed Forces Insurance (AFI.org). We've had personal-property policies and homeowner's policies with them for over 25 years. Admittedly they're not very good at avoiding losses in hurricane-prone areas, let alone making money, and they may start restricting policies or jacking up the premiums. But they offer good service and we've only made a few claims.
AFI doesn't issue auto policies directly, but in Hawaii they partner with Progressive.
We have our auto insurance with USAA (nearly 30 years). They're a lot cheaper than GEICO & Progressive and we haven't had a rate increase in at least two years. Currently USAA won't issue homeowner's policies in [-]hurricane[/-] Hawaii unless it's a first-time purchase, but when they were writing policies they were more expensive than AFI. But then USAA is probably a lot more financially stable than AFI.
We have umbrella liability insurance with AFI. They don't quibble about the auto policy being with USAA but they require a certain minimum level of auto liability before the umbrella kicks in. Never had to make a liability claim and I hope we never do.
USAA's umbrella liability insurance is way more expensive than AFI.