Happens all the time !! I think in this case, it will find the correct owner very quickly.

I always to an equipment check prior to;
a) Departure from home
b) Departure from surf/water location / carpark location...

Location A) At home, check you have the correct board/s, correct paddle if SUP, correct wetsuit, or boardies/rashie, depending on season, 1x1.25 coke bottle of water for drinking and rinsing, legrope if using an under ultilised board, etc... and even 1 beer if it is an end of day trip.

Location B) check around the car, make sure nothing is left behind, quick check of the roof, to either check secured equipment, or mates shoes left on roof, etc... and I always check for my paddle, because I read about lost paddles here every so often !! Check wetsuit has been packed into car, etc...

Location A check is maybe 1 minute, or 2 minutes if refilling water.
Location B check takes maybe 15 seconds (this is the most important check !!)

Simon