Well, I needed to install an application that required setting permissions on a comfig file. Imwas on a Windows hostingnplannon GoDaddy, which doesn't allow setting permissions. So, I decided to move the account to a Linux plan.
One thing I will say about GoDaddy, is I was able to do this all online once I figured out the weird menu options. But I didn't have to cancel one, and startma new one or set up the database again or open a support ticket.
Anyway, after this migration, and short story long, the email from names now come though to me email client from the website contact form. So it must have been something about the particular PHP configuration on windows server.