For example, when I push branch to GitLab or Bitbucket, I see such message:
Total 0 (delta 0), reused 0 (delta 0)
remote:
remote: To create a merge request for branch-name, visit:
remote: https://gitlab.com/username/reponame/merge_requests/new?merge_request%5Bsource_branch%5D=branch-name
remote:
To gitlab.com:username/reponame.git
* [new branch] branch-name -> branch-name
Is there easy way to add such message for GitHub?
That message comes from the post-receive hook configured in the remote repository. It is part of the software running on the Git server.
Unless you can modify the code on the server (GitHub), no you cannot customize it.