Seems to me the old name did rather limit their scope.
“For years, as the national cycling charity, we have worked hard to achieve three things: to inspire people into taking up cycling of all forms, be it touring, commuting, or family rides; we campaign to protect cycling interests, for example creating well designed and properly funded space for cycling; and finally, we help people to overcome personal barriers to cycling, like physical disabilities or economic barriers."
If those are their aims - and they seem like worthy aims - then the old name doesn't seem terribly appropriate. Not that I really give a monkey's one way or another. Which could be telling in itself, I guess...
(As an aside, it occurred to me t'other day that the UK's two biggest motoring organisations - the RAC and the AA - both incorporate in their names a word for 'car' which as far as I know has only ever been used by our poor benighted brethren over the pond.)