Please have a seat and wait until your name is called.
Literal
Name [object-を] called [until-まで], chair [at-に] sit honorable-wait please.
呼ばれる is the passive of 呼ぶ ('call'). 椅子にかける ('sit on a chair') uses かける in the 'sit down' sense — yet another sense of this polysemous verb. お待ちください is the honorific request form of 待つ. Receptionist register, typical of offices and clinics.