I am trying to put some money in a restaurant business under someone's name. How risky is it? Can I have my name under the business or not? what if they took all my money and say I never invest money on their business?

don't invest a dime without making any legal documents that proves your investment. Make it clear on the document that you are investing, not just lending money. Had a very crazy scene with one of my friends , who invested in a store with his relatives.

restaurant is very involved business. it would be better if you could setup a paperwork mentioning the work-division (if any), how much are you investing and a provision to get out of the deal if things doesn't work out between the partners.
if you are in some sort of visa, i heard somewhere that you could make an investment on any business like you could legally own property... better if you discuss in details with your partner and lawyer.