Git pushing to remote branch
git push --set-upstream origin <branch_name>_test
--set-upstream sets the association between your local branch and the remote. You only have to do it the first time. On subsequent pushes you can just do:
git push
If you don't have origin set yet, use:
git remote add origin <repository_url> then retry the above command.
Simply push this branch to a different branch name
git push -u origin localBranch:remoteBranch
If you don't want to set-upstream, just
git push origin localBranch:remoteBranch
First, let's note that git push "wants" two more arguments and will make them up automatically if you don't supply them. The basic command is therefore git push remote refspec.
The remote part is usually trivial as it's almost always just the word origin. The trickier part is the refspec. Most commonly, people write a branch name here: git push origin master, for instance. This uses your local branch to push to a branch of the same name1 on the remote, creating it if necessary. But it doesn't have to be just a branch name.
In particular, a refspec has two colon-separated parts. For git push, the part on the left identifies what to push,2 and the part on the right identifies the name to give to the remote. The part on the left in this case would be branch_name and the part on the right would be branch_name_test. For instance:
git push origin foo:foo_test
As you are doing the push, you can tell your git push to set your branch's upstream name at the same time, by adding -u to the git push options. Setting the upstream name makes your git save the foo_test (or whatever) name, so that a future git push with no arguments, while you're on the foo branch, can try to push to foo_test on the remote (git also saves the remote, origin in this case, so that you don't have to enter that either).
You need only pass -u once: it basically just runs git branch --set-upstream-to for you. (If you pass -u again later, it re-runs the upstream-setting, changing it as directed; or you can run git branch --set-upstream-to yourself.)
However, if your git is 2.0 or newer, and you have not set any special configuration, you will run into the same kind of thing that had me enter footnote 1 above: push.default will be set to simple, which will refuse to push because the upstream's name differs from your own local name. If you set push.default to upstream, git will stop complaining—but the simplest solution is just to rename your local branch first, so that the local and remote names match. (What settings to set, and/or whether to rename your branch, are up to you.)
1More precisely, git consults your remote.remote.push setting to derive the upstream half of the refspec. If you haven't set anything here, the default is to use the same name.
2This doesn't have to be a branch name. For instance, you can supply HEAD, or a commit hash, here. If you use something other than a branch name, you may have to spell out the full refs/heads/branch on the right, though (it depends on what names are already on the remote).