行政服务中心 (xíngzhèng fúwù zhōngxīn): administrative service center

行政服务中心 (also called 政务服务中心) are one-stop government buildings where residents handle multiple permits - marriage registration, ID cards, tax, business licenses - at a single site. The 最多跑一次 ('no more than one trip') reform campaign launched in Zhejiang in 2016 made these centers much more efficient.

register

This is formal bureaucratic language. In casual speech people just say 政务中心 or describe the errand: 去办事 ('going to handle paperwork').