Alternative ways to find out your auth realm:
Command line SVN:
svn --no-auth-cache --config-dir invalid info proto://host:port/path/to/repo will show the auth realm, possibly after asking you to accept the certificate temporarily.
$ svn --no-auth-cache --config-dir invalid info proto://host:port/path/to/repo
Authentication realm: <proto://host:port> VisualSVN Server
Password for 'danielbeck':
(invalid is the name of the directory – --config-dir – to get SVN client config from; in this case, should be non-existing dir, resulting in ignoring existing preferences like saved credentials). The dir will likely be created, just delete it afterwards.
Check the server config
If you use svnserve to serve the repo, check the realm directive in the [general] section of /path/to/repo/conf/svnserve.conf.
Patch the Subversion plugin
Unfortunately, logging is lacking in the current version of the plugin. This patch adds logging of URL and realm to auth attempts (logger hudson.scm.CredentialsSVNAuthenticationProviderImpl, level FINE):
https://github.com/daniel-beck/subversion-plugin/commit/e210707cef0dd419af4c0e4f409f0a16ef942156
Ask your SVN admin
Seriously. They'll know. (If you're the admin, well, maybe you shouldn't be.)