Roy, Royce, Royal, and Rory are all in the US Top 1000, where they join a plethora of surname-inspired names ending in -son. Royson is a new consideration, with a smart, handsome feel to it, combined with a touch of the floral. 
 
The meaning of Royson depends on which root you follow, but possibilities include: "son of Roy", Roy being an anglicized form of both he Scottish name Ruadh meaning "red" and the French Roi meaning "king"; "son of Royce", where Royce is a medieval form of Rose; and "from Royston" a British place name, meaning "town of Rose".
 
The name has yet to rank in the popularity stats, but may see use in the future. Whether it's used for boys thanks to its -son ending, or for girls, thanks to its association with roses and its similarity to Roisin, is yet to be seen.

Names That Mean Red or Redhead

Scottish Last Names

Last Names as First Names

Names That Mean Flower

Royson

Royal and Rory are both in the US Top 1000 for girls where they join a number of surname-inspired names ending in -son, from long-time favorite Madison to the newer Emerson. The yet to rank Royson could be a new consideration with its rosy feel, but tougher edge. 
 The meaning of Royson depends on which root you follow, but possibilities include: "son of Roy", Roy being an anglicized form of both he Scottish name Ruadh meaning "red" and the French Roi meaning "king"; "son of Royce", where Royce is a medieval form of Rose; and "from Royston" a British place name, meaning "town of Rose". 
Whether Royson takes off as a unisex name, or whether it leans more feminine or masculine is yet to be seen, but it does have potential.

Royson

Royson Origin and Meaning