When a user is invited to create an account, the user's name does not show up in the Customers List. This article explains why this occurs and what needs to be done.
You navigated to Manage > Customers -> Customer List but you were not able to find a customer you had previously invited. Even when selecting 'All' or performing a search the name fails to appear.
This occurs as the user has not yet created an app account (hasn't completed his/her profile).
There's no specific action you should take. As per design, the Customers List shows the users that have created a profile having accepted the invitation or the users you have manually added.
Optionally, you can send a reminder to the user you cannot find on the list, so he/she will accept the invitation and create a profile.
Once the user creates the profile, the account will appear within the group "ALL" of the customer list (and the group you had assigned upon creating the invitation) as shown in the screenshot below: