Richard, Junior and Naming Considerations
Of course, Rev. Denton was well steeped in the bible after years of religious education at Heath Grammar School and then Cambridge. I suspect John Favor was a tough taskmaster. Not only was Favour the chaplain to Tobias Matthew, the Oxford President and Chancellor and Archbishop of York, he was also assigned to debate Henry Walpole at his trial in York. Walpole was an English lawyer turned Jesuit priest who returned to England intending to convert the queen to Catholocism. During Walpole's trial in York, Favour was assigned to debate him in public. Favour also debated other Catholic priests who were captured, tortured and then later put to death. "The Story of Old Halifax," Hanson (1920), p. 105. https://archive.org/stream/storyofoldhalifa00hansrich#page/n3
In the course of his religious education, Rev. Denton would have learned about the seven deadly sins of which pride was the worst. And he would have learned about humility, the opposite of pride, which St. Augustine described by saying "Both learner and teacher need to be humble, because they learn and teach what ultimately belongs to God." Rev. Denton certainly studied St. Augustine.
Wikipedia re Pride: https://en.wikipedia.org/wiki/Pride
Wikipedia re Humility: https://en.wikipedia.org/wiki/Humility
I can imagine Rev. Denton thinking that his own name was not sufficiently religious for his first sons. According to BehindTheName.com, Richard is a Germanic name introduced in England by the Normans and meaning "brave power." The name Richard does not appear in the Bible. And I can imagine Rev. Denton thinking that naming an early son after himself would reflect pride rather than humility. And, this was an era when Puritans liked to give their children Biblical names.
Naming his first son Tymothie, however, has a religious context that reflects Rev. Denton's Presbyterian theology. Presbyterianism derives its name from the form of church governance which is by representative assemblies of elders. Saint Tymothie accompanied Saint Paul on his missionary journeys and Tymothie was ordained by the presbytery or local council of presbyters in Derbe and Lystra. Paul himself wrote to Tymothie:
"Neglect not the gift that is in thee, which was given thee by prophecy, with the laying on of the hands of the presbytery" (1 Timothy 4:14).
Saint Paul himself took part in Tymothie's ordination.
BibleStudyTools.com: https://www.biblestudytools.com/dictionary/timothy/
I suspect Rev. Denton was well aware of this history of Saints Paul and Tymothie when he chose that name. I suspect he was also aware of the religious connotations of the other names he chose for his children as described below.
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From BehindtheName.com
https://www.behindthename.com/
Nathaniel
From the Hebrew name (Netan'el) meaning "God has given"... It is borne by several minor characters in the Old Testament, typically spelled Nethanel or Nethaneel. In the New Testament this is the name of an apostle, probably another name of the apostle called Bartholomew.
Samuel
From the Hebrew name (Shemu'el) which could mean either "name of God" or "God has heard". As told in the Books of Samuel in the Old Testament, Samuel was the last of the ruling judges. He led the Israelites during a period of domination by the Philistines, who were ultimately defeated in battle at Mizpah. Later he anointed Saul to be the first king of Israel, and even later anointed his successor David.
As a Christian name, Samuel came into common use after the Protestant Reformation.
Daniel
From the Hebrew name (Daniyyel) meaning "God is my judge"... Daniel was a Hebrew prophet whose story is told in the Book of Daniel in the Old Testament. He lived during the Jewish captivity in Babylon, where he served in the court of the king, rising to prominence by interpreting the king's dreams. The book also presents Daniel's four visions of the end of the world.
Due to the popularity of the biblical character, the name came into use in England during the Middle Ages. Though it became rare by the 15th century, it was revived after the Protestant Reformation.
Phoebe
Latinized form of the Greek name Phoibe, which meant "bright, pure" from Greek phoibos. In Greek mythology Phoibe was a Titan associated with the moon. This was also an epithet of her granddaughter, the moon goddess Artemis. The name appears in Paul's epistle to the Romans in the New Testament, where it belongs to a female minister in the church at Cenchreae.
Peter
Derived from the Greek Petros meaning "stone". This is a translation used in most versions of the New Testament of the name Cephas, meaning "stone" in Aramaic, which was given to the apostle Simon by Jesus (compare Matthew 16:18 and John 1:42). Simon Peter was the most prominent of the apostles during Jesus' ministry and is often considered the first pope.
Due to the renown of the apostle, this name became common throughout the Christian world (in various spellings). In England the Normans introduced it in the Old French form Piers, which was gradually replaced by the spelling Peter starting in the 15th century.
Mary
Usual English form of Maria, the Latin form of the New Testament Greek names Mariam and Maria..., a name borne by the sister of Moses in the Old Testament. The meaning is not known for certain, but there are several theories including "sea of bitterness", "rebelliousness", and "wished for child". However it was most likely originally an Egyptian name, perhaps derived in part from my "beloved" or my "love".
This is the name of several New Testament characters, most importantly Mary the mother of Jesus... Due to the Virgin Mary this name has been very popular in the Christian world, though at certain times in some cultures it has been considered too holy for everyday use. In England it has been used since the 12th century, and it has been among the most common feminine names since the 16th century. The Latinized form Maria is also used in English as well as in several other languages.
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Saving the name Richard for his last male child seems more in character with Rev. Denton's religious education and devotion.