Large low Earth orbit (LEO) satellite constellations are intended to provide global low-latency high-bandwidth Internet connectivity. Due to their large scale and high mobility nature, networking is a big challenge. In this paper, we investigate applying Named Data Networking (NDN) to this scenario. Specifically, we discuss that NDN's architectural benefits, such as adaptive forwarding, in-network caching, off-The-grid communication, data mule service, in-network/edge computing, mobility support, and data-centric security, make it a promising candidate. Moreover, we focus on studying NDN's consumer mobility support. Specifically, NDN's in-network Interest retransmission can quickly react to satellite handovers. However, we make an observation that Interest routing paths before and after satellite handover may not overlap, hence underusing NDN's in-network caching. Therefore, we direct retransmitted Interests due to handovers to the previous connected satellite via forwarding hint. Simulation results show that the studied approaches can decently improve the consumers' performance and reduce the network traffic, achieving better consumer mobility support.