To minimize the amount of typing, it's probably easiest to do it in two steps. CD to the directory, then move.
If you only have one command, you can use a subshell:
$ (cd blob/a_long_directory_name/c/ && mv x.x y.y )
That means the `cd` will only take effect in the subshell, the `mv` will only happen if the `cd` succeeds, and the working directory of your current shell won't change.
If you have more than one command, use the directory stack.
$ pushd blob/a_long_directory_name/c/
$ mv x.x y.y
$ mv z.z q.q
$ popd