This is important because you want to know who will actually do the work on your site.
Getting to meet the web designers or the web development team is a very big part of the process of designing a perfect site for a client.
The best web design agencies out there will have zero problems in letting you get in touch with the actual web designers.
In fact, for several projects, they will want this to happen because they know it is the only way to guarantee the client will receive exactly what they want.
Getting information about the web designers can be done in many ways.
In some cases, they are presented on the agency website, in the About section.
Even, in others, you have to ask.
If, you cannot find information in this way, it might be available when you browse LinkedIn pages for the web design agency as you can see who is employed.
This is a great way to check the experience and expertise of the actual designers the agency has.