I`m a Presho, and have been researching the Presho family for some time now. I`ve found quite a number going back to 1654 in the same geographical area as Marykirk, ie between Brechin and Stonehaven, so clearly Presho and Preshaw are alternative spellings of the same name. The name Presho disappears from Scotland entirely after 1746, though whether this was due to Culloden, the Land Clearances, or they were part of the Covenant mission to send Protestants to Ireland I don`t know.
An Isaac Presho came over to England in the early 1800`s and settled around the Wigan area, and essentially, all the Preshos are descended from him. I have a pretty comprehensive list of them all if anyone is interested.
There are numerous Preshos in the USA, most of whom are descended from Peter Presho born c1705.
I`m really curious to know the derivation of the surname, though no doubt it`s lost way back in the mists of time. I think the Preshaw estate in Hampshire is just a coincidence, as there is no other evidence to link the name. I worked in Norway for some time and asked various experts if the Presho/Preshaw name could be Viking in origin, but those sequence of letters and sounds are not at all Nordic. There are a lot of Prasha names in the USA, which originates in Germany, and most emigrated in the 1880/1890`s. There are still a few in the area which was East Prussia but is now Poland, though the spelling has changed. I think it`s unlikely there is any connection with NE Scotland though.