From Old French plat meaning “flat, thin”, from Late Latin plattus, from Greek πλατύς (platys) meaning “wide, broad, flat”. This may have been a nickname or a topographic name for someone who lived near a flat feature.
Means “plank”, from Old French, itself from Late Latin planca. This could have referred to a person who lived by a plank bridge over a stream, someone who was thin, or a carpenter.