Garry My thought on the language name Objo vs ObjoBasic is that anyone kicking the tires is going to figure out it's a Basic dialect and if they are a Basic "snob" then they will turn away in any case.
The only reason to drop Basic from ObjoBasic would be the hope to defer the language question long enough that people would at least look and be impressed by the dev environment and multi-targeting enough to overcome any language concerns. And if you lead with "cross platform from a single code base" I think that will help. As for the language itself -- if you initially describe it in terms of what it provides ... clean, simple, friendly syntax but lots of stuff in reserve if and when you need it (lamdas, closures, extension methods, just list a bunch of modern / powerful stuff like that, that perhaps the reader doesn't normally associate with Basic) and make the Basic-inspired syntax kind of secondary, I think that will help too. I think your challenge is to try to draw them in and mention the dreaded "BASIC" at the last possible moment. I think that will help overcome bias in SOME people at least.
When the product matures to have .NET and other forms of interop, that will also be something of a counter to any language concerns. If Objo[Basic] will get them 95% of the way there for some ambitious project, and they're concerned it's missing some beloved thing from their current language or platform, and they know they can call into that as needed ... that should be a comfort.
I guess on balance I lean a little bit toward renaming ObjoBasic to Objo, except that there could then be some practical confusion between Objo the language and Objo the IDE / platform. But a little care in wording should take care of that.