Is it a good idea to ask your designer to recommend builders?

By all means, collect any recommendations that are offered. If anyone does recommend builders to you, you need to subject those recommendations to your own rigorous filtering process. In my experience, you can’t beat meeting the builder yourself and taking the time to visit completed projects. In addition, you need to follow up any references and ensure that the builder you choose has experience with jobs similar to your own. It’s not a one-way process though; the relationship between you and your builder needs to be good for both of you.