What does Prothero surname mean?

I did not write the following. However I have researched this and they have written most everything I have in my notes for this name. If you would like to research other names I have linked to their site for others to use.
Last name: Prothero
This notable and long-established surname is of early medieval Welsh origin, and derives from the ancient Welsh male given name "Rhydderch", a compound of the elements "rhi", ruler, and "derch", exalted. This name was borne by one of the North British rulers (flourished 590), Rhydderch Hael, called Hen, who fought with Urien, leader of the Britons in the 6th Century. In medieval documents of Wales the name is variously referred to as "Rodarchus, Rodercus" and "Rederech". The forms "Prydderch, Prytherch, Protherough" and "Prothero(e)" result from fusion of the Welsh patronymic suffix "ab, ap" with the name. In some instances, the Germanic personal name "Hrodric, Rodric(k)", from "hrod", renown, and "ric", power, replaced "Rhydderch", as a result of falsely equating the two names. An instance of the Anglicization of Rhydderch into Roderic occurs in the last century a propos of Pen Glasi, near Aberystwyth, "the present house was built by Roderic Richards, his father was Richard Rhydderch". One John ap Redragh was recorded in Caernarfonshire in 1538, and in 1581, William Prythergh, Proterugh or Protherough was entered in the Oxford University Register. On September 19th 1590, Elizabeth Prothero married a John Brown in Ludlow, Shropshire. A Coat of Arms granted to the Prothero family is a shield chequy azure and gold with a red annulet. The first recorded spelling of the family name is shown to be that of Treharn ab Retherech, which was dated 1292, in the "Subsidy Rolls of Cambridgeshire", during the reign of King Edward 1, known as "The Hammer of the Scots", 1272 - 1307. Surnames became necessary when governments introduced personal taxation. In England this was known as Poll Tax. Throughout the centuries, surnames in every country have continued to "develop" often leading to astonishing variants of the original spelling.

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Addition of my own notes:
Recording of the surnames was left to people that were literate. Usually parish leaders. Variations due to the imprecise or improper recording of a name occurred for many years. The original name was Brythonic Celtic, known to the Welsh as Cymraeg. When translated to English changes were often dramatic. Sometimes spelling variations were according to the individuals job. It could be a branch loyalty within the family, a religious adherence or a partiotic affiliation. I have seen the name spelled in various way; Prothero, Protheroe, Prytherick, Prothers. Going through records I realise that my family line's name changed occasionally. (Not only this line, but many lines.) The name is found in Carmathenshire. This is were they held a family seat from the ancient times. Some say it goes back to the time of the arrival of Duke William at Hastings in 1066, others say the Norman Conquest.
Many Welsh arrived in North America in the 1800s and 1900s. My direct line, grandmother, in the 1880's. (Her father was not a Prothero, her mother was.) They came her to leave the "tax man." (If you are a family member and do not know the story, contact me.) The people were seeking work, land, and freedom from the rulers of the Great Britain continent.