In my brief research, it appears that in most cases it's okay to name a piece of software the same name as another existing piece of software as long as it's in a different market.
Does that seem true?
For example, I see several with the name 'Coda', and 'Eclipse'. And those were just the first two names I picked to try.
I have name for my software that I think really fits well, and it is in use by a couple other small-ish pieces of software but they are in totally different markets. Of course I'm hoping my software will make some waves, but I'm not expecting to be the next Microsoft (nor would I want to be ;).
How much would you worry about this?
It probably apply only to non registered trade marks or to words that are in dictionary. "Made" words is probably difficult to use even in other markets. For example eclipse is dictionary word (you know something about the sun :).
From a non-legal perspective, if the other product aren't well known then it might be okay, but it's still probably better to use something at least slightly different.
If it is well known or you suspect they might become well known (more so than your own product) then it could cause confusion among your users, like when they do a Google search for instance, yours better be in the #1 spot for your own product name.
Even if yours will become more well known, you're also possibly going to hurt their branding even though they're not a competitor to you. This may or may not matter to you, but it's something to think about whether you'd like someone else doing the same to you. (Or maybe they do get big and you're the one who's brand is hurting)