For GitHub, using the hub[1] client, you can simply do:

  hub create -p

That will create a new private repo, matching the name of your repository.

What I will often do if I want to instantly mirror something to github:

  hub create -p --remote-name=github

Which will create a new remote with that name. Otherwise origin will be used, which can conflict if you already have an origin remote.

It is also less typing.

[1]: https://github.com/github/hub