Yes, this is a kind of twitter 'follow' use case.  Here is a good plugin that implements this mutual approval.

http://community.elgg.org/plugins/728303/1.5/friend-requests-elgg-18

You are right, but need change name for "follow" or something like...else people that comes from facebook will become confused...

You can do this with Evan's plugin:

http://community.elgg.org/plugins/724666/1.0.1/followers-for-elgg-18