Its really a matter of marketing. Think about proctor and gamble, for example. They produce tons of different products, but their name isn`t anywhere readily visible on their products. They`d prefer to market based on the product name rather than their total brand. This can be for many reasons. One reason could be that if you make both food products and liquid bleach, you probably wouldn`t want to advertise that, because customers might get this fear or vision that bleach would be entering into the food you produce.
So to answer your question, if the two businesses you have offer products that you might not want to be associated together under the same name, use different names. On the other hand, if you don`t mind that these products are associated together, as it will do no harm to the others image, AND you`d like to capitalize on your already established good name, than you should use the same name.
Motivation for Entrepreneurs