Hello David,
I agree with the Hebrew translation, but not the Alexander name adoption theory, my grandmother was surname Alexander and in Poland the surname Alexanderowicz going back to around 1800, Alexanderowicz simply means 'of Alexander', my understanding is yes it is a very Western name, but Alexander the Great was much admired by old time Jews as he was considered a friend and protector and many Jews in the 18th and 19th Century were name Alexander long before they came to Western countries.
So would disagree Alexander is a Jewish name for some time.

Regards,
Malcolm Katz
London