Tried looking in github, project-specific pages, wikipedia and still have no clue:

What does OMR stand for?

runtime?

Doesn't seem to stand for anything (at least it's not defined in the project charter).

If I had to guess at it:

Open Meta-Runtime

But I could see how that might be misinterpreted compared to their goals. Not all cap names are acronyms?

https://projects.eclipse.org/proposals/omr

It stands for Open Managed Runtime.

Is the Open really open, as in acceptable license that won't hold it back from gaining adoption in OSS and Enterprise community - or - are there licensing, patents or other proprietary strings attached?

OMR is under Apache License. https://github.com/eclipse/omr