I just signed up for Alexa Pro.
If people go to
mydomainname.com, will they know that whether or not the domain is registered in Alexa Pro?
Based on their plans and pricing page, the benefits that you get are information and statistics about your website. There doesn't appear to be anything such as site badges that would let visitors to your site know that you have signed up for the pro service.
I also cannot find a page where Alexa publishes a list of their Alexa Pro customers.
You could let your visitors know that you use Alexa Pro, but other than that there doesn't appear to be an easy way for them to find out.