Pi-hole admin inconsistenty appearing

Wikipedia has comprehensive general information on hostnames.

It's a bit out of scope for Pi-hole (but click for more to get you started)

The basic principle is the same:
A device in your network has a label name (e.g. laptop), and that name can be extended by a domain (i.e. lan), separated by a dot.

Note that a device can be associated with multiple names, as your device's OS might claim a name for itself, your router may indepedently attach a name to it, and Pi-hole can do that as well (also partially discussed in How to show readable hostnames when Conditional Forwarding supplies only gobbledygook).

The local domain name part (i.e. lan in your case) is commony provided by your router and sometimes referred to as search domain.
While Pi-hole's DHCP server provides a field to change that name, most consumer-grade routers won't allow you to do so, so you'd have to live with that domain name.

Note that Pi-hole's Query Log doesn't show device names, but rather clients based on their IP addresses. For that reason, a device may show up as multiple clients in Pi-hole, e.g. if it had more than one network adapater (WiFi and Ethernert) or more than one IP address (IPv4 and potentially several IPv6).

Things get a little more complicated when you own a public Internet domain and want to use that in your internal network as well.
While this is beyond Pi-hole, a search in these forums may well yield some user's recommendations on how to achieve this.