Eh … whenever someone mentions Square I first think of Squarespace. That’s the much more present Square brand in my head (probably because I listen to way too many podcasts and Squarespace seems to advertise on all of them while Square isn’t relevant or present at all in Germany).
Their brand name really manages to confuse me whenever it’s mentioned … but that just comes with the territory of picking something so generic.
So, yes, there is a question what someone is referring to when they talk about Square in the context of an app. That happened to me several times already, here on HN. I read some headline with Square in it, click on it and am confused why it’s not about website hosting.
I have little doubt that it is possible to build an extremely successful brand that no one confuses with anything else around a very generic term (just think of Apple), but if you want that super-generic word to work out for you (and those words can be cool to use, no doubt) you have to live with people confusing you until you pull it off. It’s a trade-off.