You may have heard of DCI numbers, seen them in other players’ logs, or your DM told you their DCI number for your logs.
Adventurers League does not require you to register or receive any kind of registration number.
DCI numbers are from earlier days of Adventurers League. They are also used in Magic: the Gathering games.
Players and DMs used to get DCI numbers. Local game stores would use them to record attendance.
They may tell you their DCI number for your AL logs, but you are not required to record it. Some players still like to record it in their AL logs.