Honestly Neuromancer didn’t factor explicitly in picking the name, other than through ambient connotations. Or for that matter Doctor Who, which used the name to describe the Timelord’s computing system on Gallifrey :)
I had forgotten the Dr Who reference, though I only dip into Dr Who now and again. I had always assumed that the title of the film 'The Matrix' was in homage to Neuromancer. I had never considered that Gibson might be doing a homage to Dr Who.