As amusing as this is, unless either name is a registered with an appropriate regional authority program or is trade-mark copyright then another company or person with such a registered name can sue them.
You are allowed to use your own name and apply it to represent yourself, but when you come to expanded practices such as applied business, the name by which your "company" is recognised is not the same as your personal name or title (unless you are self employed and clearly refer directly to yourself and not a greater whole). The computer company Dell is a registered trade-mark. I am unsure whether Mr Dell's company nams are registered or not, but if they are then technically "Dell" shouldn't be able to sue him as it is a seperate and recognised brand name.
This is also partly against rules of "fair trade" recognised and established by various international copyright and trade agreements/treaties.
