I think it would be better giving free software _any_ name, some kind of
"nickname".
It could be really stupid. Take "freest" as an arbitrary example.
Whenever you mention using "only freest programs", everyone will ask "oh what
is this?".
When they hear "free software" they don't listen, because they think they
already know what this is - gratis, free of charge software, freeware.
I was using "linux" (I thought I did) for many years, browsing blogs and
forums, without noticing the difference of free software or open source, even
without knowing the name of my operating system!
That was not my fault. Everyone said "linux" and talked about "open source".
Compared to how many people are in my social environment, nearly no one knows
about it (and I mean really knows about it), so I think it's an unknown
movement.
Sad about this: the percentage of people using free software is slightly
higher (for example many collegues at university used libreoffice) but they
just don't know about the ideas behind free software and its benefits!
This _is_ a problem.
