The Pleasaunce is a word of French origin. One of the first recorded uses in this country was by Henry V when he built a moated summer house at Kenilworth Castle. It also was a Tudor name for the then Greenwich Palace and Park from around 1450, when it was named by Henry VI's wife Margaret of Anjou.
Henry V's brother, Humphrey, Duke of Gloucester, Regent during the minority of Henry VI, realised the strategic importance of Greenwich. Humphrey obtained the manorial rights and in 1428 decided to build himself a palace. It was of modest design, built of red brick on the site of the Old Royal Hospital. After his death, the land was seized by Margaret of Anjou, wife of Henry VI and renamed the Palace of “Pleasaunce” or Placentia. and called it "Placentia," or "my manor of Pleasaunce."
It could be this combination of Tudor connections, Greenwich history and a moated house oif Kenilworth which prompted a local headmistress to suggest 'Pleasaunce' as a name for the gardens which were created after the council bought Well Hall in 1930. The Well Hall Pleasaunce shares the name with a road in Edinburgh, the East Greenwich Pleasaunce and a building now used as a Christian holiday home in Norfolk.
Its etymology suggests that 'Pleas' comes from 'pleasure' and 'aunce' to imply 'a state of'.
When William Roper, builder of the Tudor Barn - then an outbuilding to the main manor house within the Moat - inherited the estate, it was described in his father's will as 'Welhaw' and 'Welhawe'. Variants of these names are found written in the 15th century as 'Wellhaw', 'Wolhall' and 'Welhalle' used to describe the estate and dwelling. There is nothing to indicate the name is connected at all with 'wool' and the assumption must be the name refers the place as being a source of water.