'Cycling' will be more inclusive to other activities that are sufficiently closely related to 'bicycles' and/or 'bicycling' but are often considered distinct, e.g. unicycling, tricycles, quadracycles, different kinds of scooters.
Nah - pretty much anyone who rides something esoteric will have ridden a conventional bicycle too.
Also users find SE by search engine, and google knows us by name.
Finally, ngram suggests that bicycle is a more common word than cycle.
Perhaps a cname or some other kind of redirect would be useful, but a site rename is not.
Problem is that would include motor cycle.