What does custom mean? Adjective: Made or done to order for a particular customer.
Most dog houses in the marketplace are a pre fabricated kit or a complete construction, like the plastic type found in the large retail stores.
In fact when it comes to most dog houses especially those that are considered off the shelf there is no customizing options available, these type would not be considered custom dog houses.
These are considered to be what you see is what you get; however there are some doghouses that are designed to be customized to some degree.
For an example luxury dog houses like the Victorian model pictured to the right does not come with paint, rain gutters or shingles (shipping would be impossible) so you can customize it to match your own home or choose the colors that appeal to you.
You can also have the door customized to fit your dog if for some reason it doesn't work for your particular breed as it is offered. There are other options for some houses like an insulation package or a heating cooling option.
Depending on the builder and the circumstances you can have some unique options available for you; it would depend on the degree of customization you desire.
Most dog house builders use jigs for building their homes and are usually not open to modifying them for a different design.
A private local builder would be the best option for a custom dog house because you can be involved in the design process and request specific parameters.
However the more demands you place on the build the more expensive the house can be.
Finally there are several different design options available to you once you have the house assembled and configured in your yard, which could include planters or a walkway.