Well, its obviously code for something. I would suggest a security code like all the command officers had.
"Recognize Picard, Zero Alpha Three".
That's my best guess, anyway.
But, it sounds weird to say a security code between your rank and name. I can't remember hearing anyone saying that in other Trek episodes.
No First Name No Middle Initial Data.
(Some of my relatives have only a first and last name, and NMI appears on their official documents)
Anyway, I'd think that Data would be his first name. If he had a full name, it would presumably be Data Soong, considering that Noonien Soong is regarded as his "father."
To be honest, I always thought of Data's full name was "Data." Kinda like Cher or Madonna... even though that isn't really their full names, lol.