What is a standard or conventional name for a column representing display order?
It depends on what your philosophy is around column naming.  

If you go for very descriptive long column names, then display_order is perfectly fine, since that is exactly what your column contains.  

If you are comfortable with shorter names that may seem a little cryptic, but which can be figured out pretty easily, then you could use seq or ord.  For English speakers, seq is pretty unambiguous as there aren't a lot of words that this could reasonably represent.  I would pick that over ord for that reason.