Hi there. 

Your Customer Directory will find duplicate profiles if two or more customers have the same email address and/or phone number. However, if the profile names are dissimilar or if the two profiles have a different email or phone number, they will not be identified as duplicates. In this case, you can still manually merge the profiles if they happen to be the same customer.

In regards to your client not being able to book more than one appointment, what was it that they were running into? Did they get any error message of any kind?