You should report to Social Security any changes that could affect you or your family members’ disability benefits. The most important thing to report is when you return to work, even if it's only for a few hours or a small amount of money. Working can affect your medical eligibility if you earn over a certain amount, and for SSI, earned income will lower your SSI benefit.
It can be difficult to know what changes in your life can affect your benefits, but especially for SSI, err on the side of caution. Changes in your living situation, assets, income, marital status, and your state of residence can all affect the amount of your check and even your eligibility. And if Social Security pays you more than you should get, you'll have to pay back the overpayment.
And of course report the practical changes as well: changes of address and bank account so that Social Security can contact you and pay you properly.