How to know who is the maintainer of a GitHub repository?

Team privileges are not public in general. Even an organization-membership is not public since the publicity must be chosen by the given member, as the Documentation states:

,,By default, your organization membership visibility is set to private. You can choose to publicize individual organization memberships on your profile."

This partly applies for their implementation of CODEOWNERS, too. If it is up to date the given source file is annotated with a link to its responsible GitHub user.

However there's normally no need to know the individual maintainers of a repository (since every interaction with repos you're able to access is covered by the GitHub UI, which also assures that somebody takes care about your request). If your attention is about a public repository you might search the commits for accepted pull-request. But in that case you would preferably fork the repo and just generate pull-requests on your own.

You are even not able to contact an organization via GitHub - try to find their official website, contact them and ask for their maintainers if you need that information.

GitHub (since July 2017) now officially supports "code owners" for projects. Code owners are individuals or teams that are responsible for code in a repository.

Project maintainers can add a CODEOWNERS file to their repository to make it easier for others to identify code owners and have code owners be notified to review Issues and Pull Requests.

See the announcement post and help article for more info.