Heloc for paid off house, questions

[Robert S Struhala Jr]

Hello all! The house my Wife and I live in was purchased subject to. We have decided to pay off the balance so we would have a free and clear deed in our names and get a heloc. Would the heloc have to be in the name of whoever the deed is? I was considering putting it in both our names for potentially better protection if someone were to ever sue one of us individually. Her income is 1099 so I’m not sure if that would be an issue. My income is w2. Both have credit around 800 with just about no debt. Looking for some pointers or just pointed to the right direction. Thanks!