A HELOC on a house owned by two people usually gets underwritten on both people. That isn't always required, and where it isn't, the choice matters more than it looks.
Both incomes on the application means a bigger line of credit, most of the time. Both credit scores get pulled, and lenders typically price off the lower of the two middle scores, so a spouse with a 640 can cost you the rate the 780 would have gotten alone. Run it both ways before you apply. Some lenders will let one owner borrow while the other signs only to pledge their interest in the property, which puts the debt on one credit report instead of two.
The credit report effect is real for anyone planning to finance something else soon. A HELOC reports as revolving credit at many lenders, so a high balance can pull a score down the same way a maxed card does. If one of you is going to apply for a mortgage or a business loan in the next year, keeping their name off the line of credit is a deliberate choice rather than an oversight.
Divorce is where the joint version gets expensive. Both names on the note means both people owe the whole balance no matter what the decree says. A divorce decree binds the two of you. It doesn't bind the lender. The person who moves out can be pursued for a balance the person who stayed ran up, and the only real fix is refinancing or closing the line of credit at the split, which nobody wants to deal with in the middle of everything else.
Death is cleaner and still needs a plan. A joint line of credit usually survives with the surviving borrower. One in a single name becomes a debt of the estate, and the lender can freeze the remaining availability the moment they learn the borrower died. If the strategy depends on that available room, the survivor finds out at the worst time that the room is gone.
Business owners have a fourth option. A line of credit in the business name, underwritten on the business, keeps household credit clean and the interest tracked separately. It usually requires two years of returns and a personal guarantee anyway, so the credit exposure doesn't disappear, it just sits in a different place.
Whatever you pick, both spouses need login access and both need to understand how it runs. I've watched this go wrong more often from one person not knowing the account existed than from any underwriting decision.