Swair, or SWIRE, signifies the descent of a hill; and the epithet Red is derived from the colour of the heath, or, perhaps, from the Reid-water, which rises at no great distance.
"Minstrelsy of the Scottish border (3rd ed) (1 of 3)"
Walter Scott
I take Squire and Square to be phonetic corruptions of SWIRE and Swear, and Squirrell to be properly Swirrell, a diminutive.
"Surnames as a Science"
Robert Ferguson