If I use a non-default value for "Source Code Management->Git->Name of repository" in a project, the Git plug-in breaks (whereas it worked before I upgraded to 1.1.5).

This is the crux of the problem:
Caused by: hudson.plugins.git.GitException: Error performing command: git.cmd config --get remote.origin.url
Command "git.cmd config --get remote.origin.url" returned status code 1

Even though the remote is named something else than "origin" (via the "Name of repository" setting), the Git plug-in still refers to it as "origin". I have verified that resetting "Name of repository" to the default fixes my problem.