Any rule you come up with will have to be broken as your collection of abbreviations grows, because you will end up with duplicates. Bear and Noose Alley would also become BAN in your system (Initial letters of first three syllables).
The same goes for your colleage's proposal (First two letters of the first word, first letter of the second word).
In general, taking a couple of consecutive letters of a word is common, as is taking the first letters of words. I have not often encountered abbreviations based on syllables and it feels counter-intuitive to me.
When the number of letters in an abbreviation may vary, often the first letters of words are used (sometime leaving out articles), as in NATO, CIA, or HIV.
When the number of letters is fixed, often some consecutive letters are picked, but exceptions are used to avoid doubles.
For instance, in Formula 1, drivers are given a three-letter abbreviation to identify them, often simply the first three letters of their family name:
HAM -> Hamilton
ROS -> Rosberg
VER -> Vergne
VES -> Verstappen
Similarly, airports are designated by three-letter abbreviations, sometimes but not always based on the first letters of their name or location:
AMS -> Amsterdam
LEH -> Le Havre
PAG -> Pagadian
On the other hand, many of those codes are recognisable but don't follow that simple rule:
PAC -> Panama City
Some seem plain weird:
SKG -> Thessaloniki (Makedonia Airport, not Spielberg, Katzenberg and Geffen)
And some follow your rule:
PHC -> Port Harcourt
See this link for more: http://www.nationsonline.org/oneworld/IATA_Codes/IATA_Code_A.htm