Abraham 1

Even though Abraham's father and family (kinsfolk) had not hearkened to the word of the Lord, Abraham himself had a great desire to follow the Lord and receive his priesthood saying -

"...finding there was greater happiness and peace and rest for me, I sought for the blessings of the fathers, and the right whereunto I should be ordained to administer the same; having been myself a follower of righteousness, desiring also to be one who possessed great knowledge, and to be a greater follower of righteousness, and to possess a greater knowledge, and to be a father of many nations, a prince of peace, and desiring to receive instructions, and to keep the commandments of God, I became a rightful heir, a High Priest, holding the right belonging to the fathers." (Pearl of Great Price | Abraham 1:2)

For -

"I sought for mine appointment unto the Priesthood according to the appointment of God unto the fathers concerning the seed." (Pearl of Great Price | Abraham 1:4)

Because of Abraham's obedience even to the point of losing his own life, the Lord said -

"...I will lead thee by my hand, and I will take thee, to put upon thee my name, even the Priesthood of thy father, and my power shall be over thee." (Pearl of Great Price | Abraham 1:18)

With these words, the Lord made it clear that we take upon us His name or He places upon us His name as we receive His priesthood. Thus His power will be over us. Taking on His priesthood then is synonomous to taking upon us His name.

The rights and responsibility of the priesthood was so important to Abraham that he explains -

"...the records of the fathers, even the patriarchs, concerning the right of Priesthood, the Lord my God preserved in mine own hands; therefore a knowledge of the beginning of the creation, and also of the planets, and of the stars, as they were made known unto the fathers, have I kept even unto this day, and I shall endeavor to write some of these things upon this record, for the benefit of my posterity that shall come after me." (Pearl of Great Price | Abraham 1:31)

Abraham made it clear that just as Moses, he also had the record of the creation and the plan of salvation in his possession.