As a firm in the private sector, our Board has adopted the practice of not recording movers and seconders for quite some time and it has worked out well.  We only record the motion, that it was moved and seconded, how many were for, against, absent, abstain etc. and whether it was carried.  

We also do not record movers or seconders. It's a common misapprehension that moving or seconding implies support of a motion, whereas it really implies support of debating the motion.  

The only time we would record a director's name in relation to a motion is if they asked for their dissent to be recorded in the minutes.

At one of my first GPC conferences, in a session on recording meetings it was noted that indicating the names of movers and seconders was no longer a best practice.  Instead we record whether the motion was unanimously approved, or majority approved, by the Board and would also note  any where not in favor or did abstain. We also note that the motion was carried.