The name is most likely to derive from rēad, the Anglo-Saxon (Old English) term for the colour red.
[1] As a name it is believed to have originally been descriptive of person's complexion or hair being ruddy or red.
As a personal name a grammatical form of Read, Reada, was used at the earliest stages of English history.
The Readingas appear to have been named after a chieftain called Reada, "The Red One," with the addition of the element -ingas meaning "the people of.
However, this usage would have been as a descriptive by-name as inherited family surnames had not yet become established.