Seeing as your business will probably be shit and very low key, yes, you will be able to use it for the moment without attracting attention. However, in the unlikely event where you go on to achieve things and build a reputation, the other company may become irrate and eat you alive. This is especially problematic if the other company using the name is bigger than your operation, which given the circumstances is highly probable.
For advice on choosing a new name, pm politik, he's great with this sort of thing.