You (both) do have a middle name. It's just one letter in length.
An
initial in this sense, by definition, is the
initial, or first, letter of a proper name. In your cases, it happens that the initial is also the entire name.
Regarding ticketing, in my limited experience, there's no likely problem for missing the middle name. As mentioned, it's only likely to be a problem if there is
contradicting information between the ticket and ID.