Let's suppose that I have a working Shibboleth and I put <Location /limesurvey/123456>ShibRequestSetting requireSession 1 . . .</Location> to Apache configuration. Now only those with account can answer to the survey number 123456.

But can I get usernames -- that is, something like REMOTE_USER or displayName variable from Apache -- to the survey? It would not be perfect, as someone could tamper data, but that could be detected from logs if needed.

Not with LimeSurvey core.

Need a plugin : check gitlab.com/SondagesPro/OrcidAuthenticate for some sample
Particpant via OAuth

OK, thanks. I'll see if I write a plugin or do some kind of redirection trick with get-variables and panel integration.

My opinion :

Plugin check if REMOTE_USER is set,
1. if no : show a "You must be loggued in" link
2. if yes : find the REMOTE_USER in token table (attribute or ? ) : create the token or redirect to token

1: gitlab.com/SondagesPro/OrcidAuthenticate...uthenticate.php#L629
2: gitlab.com/SondagesPro/OrcidAuthenticate...nticate.php#L191-218 (but here : i use a redirect , it's not needed in your case i think).