I contacted the BMO head office for clarification.
Here's the official answer:
"I can advise that 'BMO' is the abbreviation of the name Bank of Montreal. BOM would be the abbreviation in English for Bank of Montreal; however in French the abbreviation is BDM for Banque de Montreal. Therefore, the BMO abbreviation is used as it is accepted in both languages. In addition, the Stock Exchanges have also assigned us the abbreviation of BMO."