I'll try to answer your questions as I understand them - just let me know if you would like further clarification.
- Windows determines which network adapter based on a "metric" value, defined by Microsoft as:
"A metric is a value that is assigned to an IP route for a particular network interface that identifies the cost that is associated with using that route. For example, the metric can be valued in terms of link speed, hop count, or time delay. Automatic Metric is a new feature in Windows that automatically configures the metric for the local routes that are based on link speed. The Automatic Metric feature is enabled by default, and it can also be manually configured to assign a specific metric."
- So, to change which adapter windows uses, you must manually change the metric. This can be done by opening the relevant adapter's properties from "Control Panel\All Control Panel Items\Network and Sharing Centre" and following the steps shown in the image below from left to right, noting that windows uses the adapter with the lowest metric when you enter a number in the box. (I suggest putting 1 in the box of the adapter you wish to use).
With regard to your final question, harrymc's point is important - you are unlikely to be logged onto a domain on a personal computer, domains are usually reserved for large businesses or institutions.
IP addresses are assigned by the Dynamic Host Configuration Protocol (DHCP) on your router to your interface, which identifies your interface via its MAC address - computer host name as you call it, doesn't play a part in this.
- To answer the final question of how to control the assignment of IP addresses, the most common method is to use DHCP Address Reservation which is set up on your router. This is usually a very simple process and modern routers often show a list of currently connected devices, where you can you select a device and assign it an IP address of your choice without having to follow all the steps in the linked tutorial.