[siegel]

Your assumption that they don't have a trademark may not be correct. In the US (and a number of other countries), you can get common law trademark rights by using a mark even if you don't register it. It sounds like they are using the mark we are talking about. So, they may have trademark rights already.

Doesn't mean you can't use the name. Perhaps the name is generic or sufficiently descriptive of what the software does that it can't get trademark protection. Or maybe your product is so different that there wouldn't be a likelihood of confusion.

Can't answer that question in a vacuum (don't know the mark, how they are using it, how you plan to use it). But assuming they have no trademark rights is dangerous.