The yacht designer's role varies very widely. When you talk about a totally custom design, the owner works with the yacht designer to develop the design and pays the costs involved. Then the owner or designer will bid the construction to a number of yards. Most owners retain the designer to at least minimally work with the yard during construction answering questions and providing supplimental drawings. Some owners or yacht designers chose to have the designer play a more hands on, supervisory role during construction.
Of course modern designs require a lot more care in design, and engineering and so if you are contemplating a modification to the design, if possible, it really pays to work closely with the original designer.
With regards to production boats, when my mother was developing boats, having them built and importing them, most of her boats came from Taiwan. In her company's case, she and my stepfather contracted with the yards to develop the designs, and the yards would hire outside yacht designers or use in-house yacht designers to develop the design. Once the basic design was worked out, the interiors were mocked up and then my mother and stepfather would refine the interior design, adusting locations, heights, widths and details until they were satisfied. At that point the yacht designer would be brought in to further develop the drawings into construction documents, engineer the structure, and 'balance' the design so that the boat sat on its lines
. If an owner wanted a substantive change to the production boat, the designer would draft the change, evaluate the impact on the design, and make drawings documenting any revisions to the structure or weight distribution that was required.
On the other hand, if you are talking about more traditional designs, they are more forgiving and so minor alterations to an existing design are less critical. When I worked for Charlie Wittholz in the early 1980's, we were doing a design for Cheoy Lee. Cheoy Lee gave Charlie a basic list of requirements, length, number of staterooms, general layout and so on. Charlie prepared sketches which were approved by Cheoy Lee and then Charlie's office prepared detailed construction drawings.
At some point after I left Charlie's office, Cheoy Lee made some customized versions of this boat. They worked with the customer and made minor changes in-house, but when they had a request to make more extreme revisions, they came back to Charlie and he worked with the client to revise the design accordingly.
I hope that this clarifies the Yacht Designer's role a little.