I was interested to find this thread as this problem has occurred to me for the very first time in all my years of flying. I booked with United through Flights by Celebrity and see my first and middle names are merged.
However, when I try to enter my Aeroplan number for flight points, United's system tells me the first names do not match. My first name on my Aeroplan account is correct, on the United booking is merged.
When I called for assistance, the automated system asked some questions, one being "Is your first name "first-name-middle-name" to which of course I answered no. Only then did it put me through to an agent who was adamant the first-name-middle-name merge is not an issue.
I am not convinced and will call again today and speak with a different agent.