'Sikandar' (سکندر/सिकंदर/সিকান্দর) is the Farsi way to say Alexander. The word means warrior, and was a variant of the name Iskandar, which is the Middle Eastern (Arabic and Farsi, and languages influenced by them), version of the given name Alexander. Now Urdu and Hindi were greatly influenced by Farsi from the period of the Delhi Sultans onward, so that version of the name also came into vogue in the subcontinent. Further, the name Sikandar was taken by several Muslim rulers in the subcontinent such as Sikandar Shah (the name of several sultans, in Bengal, Delhi and Kashmir), and the more famous Sikandar Lodi, Sultan of Delhi. As a result, the name 'Sikandar' was popularised.

Interestingly, one of the kings of the Mrauk-U kingdom in Burma was named Min Phalaung Sikandar Shah, despite being Buddhist. Several of his successors, also Buddhist, had Muslim names such as Salim Shah. This was probably due to his contact with the Sultanate of Bengal. So to add to your question, Bangladesh also refers to the ruler as Sikandar.

I'm not sure what sources to put, considering these claims aren't exactly related to specific historic incidents, and there really isn't too much to write. This is less of a history thing and more of a linguistic development thing.