I don’t think you are quite there with a name for it yet, but I do agree that the bible uses gifts/rewards as a an incentive for voluntary submission to God’s will. I also think that Hebrews 12:2 says that the promise of future joy is one of the of the reasons Jesus voluntarily submitted himself to the Father’s will in redemption.
Some Christians disagree, concerned that a reward/gift incentive somehow calls into question the genuineness of the motivation. But I think that has more in common with enlightenment thinking where things should be sought or avoided for the intrinsic rightness or wrongness of the thing or action itself. I don’t think we see that in the Bible.
Honor your father and your mother, as the LORD your God has commanded you, so that you may live long and that it may go well with you in the land the LORD your God is giving you. ~ Deuteronomy 5:16*,
The Lord could have said, “Honour your parents because it is the right thing to do”, but instead uses the blessings of a well-structured family as an incentive to obey. cf. Paul’s emphasis on the ‘promise’ of this verse is in Eph 6:1-3.
The beginning of wisdom is this: Get wisdom. Though it cost all you have, get understanding. Cherish her [Wisdom], and she will exalt you; embrace her, and she will honour you. She will give you a garland to grace your head and present you with a glorious crown. Listen, my son, accept what I say, and the years of your life will be many. ~ Proverbs 4:5-9
Here the Sage gives his apprentice a powerful incentive to heed his advice and pay the ‘cost’ required to grow in godly wisdom. Namely, that all things being equal, the wise are honoured by their wisdom and flourish in the world by avoiding the mistakes of the wicked. That is (one of) rewards God holds out to motivate us to diligently seek wisdom. There are a bunch of verses like this in Proverbs.
“For I take no pleasure in the death of anyone, declares the Sovereign LORD. Repent and live!” ~ Ezekiel 18:32
Here God could have said, “Repent it is the right thing to do” but instead, “life” is held out as an incentive to motivate repentance.
The clearest examples of this reward-incentive, I would say, are seen in Revelation when Jesus speaks to the seven churches:
To the one who is victorious, I will give the right to eat from the tree of life, which is in the paradise of God. ~ Rev 2:7
To the one who is victorious, I will give some of the hidden manna. I will also give that person a white stone with a new name written on it, known only to the one who receives it. ~ 2:17
To the one who is victorious and does my will to the end, I will give authority over the nations… I will also give that one the morning star. ~ 2:26-27
The one who is victorious will, like them, be dressed in white. I will never blot out the name of that person from the book of life, but will acknowledge that name before my Father and his angels ~ 3:5
The one who is victorious I will make a pillar in the temple of my God. Never again will they leave it. I will write on them the name of my God and the name of the city of my God, the new Jerusalem, which is coming down out of heaven from my God; and I will also write on them my new name. ~ 3:12
To the one who is victorious, I will give the right to sit with me on my throne, just as I was victorious and sat down with my Father on his throne. ~ 3:21
Seven times in seven letters, Jesus motivates the reader to overcome evil, sin, opposition, and apathy in the last times by holding out a reward to incentivise the one who “hears what the Spirit says to the churches” and puts it into action. Personally, I think it is amazing that God is so good and gracious that he does not want our obedience to be dutiful drudgery in cold pursuit of the ‘right thing to do’ but a delight and joy in the pursuit of a God who is open-handed and generous towards those who serve him.
All that is a long-winded preamble to say that I think Hebrews 12:2 follows the same pattern. That one of the the reasons Jesus’ agrees to submit to the Father’s will in redemption is because of the joy he would experience at his glorification. That is consistent, I believe, with the general theme of reward incentives in the Bible, and it is supported by the grammar of Hebrews 12:2. Ie. Why did Jesus endure the cross? Hebrews 12:2 says, “because of the joy set before him”.
That v3 says “Consider him who endured such opposition from sinners, so that you will not grow weary and lose heart.” Would imply that we, are to consider Jesus’ example of faith and the reward he received, so that we would likewise persevere in faith and focus on the joy that awaits us in the presence of the Father. Keeping the faith despite not yet receiving what one has been promised is the main theme of Hebrews 11:1-12:3 after all.
Finally, I don’t think we have to worry that Jesus (or others) being incentivised to submit to God’s will might somehow call into question their motivations. The LORD is the one to whom all hearts are open, he is able to see whether a person is seeking a reward as an end in itself or as a means to deepen one’s delight in his goodness and grace.
EDIT: isn’t that the whole point of giving gifts in the first place? That the giver would delight the recipients joy and the recipient would delight in the givers generosity. Lastly, this isn’t work’s righteousness I am describing because salvation is still through faith in Christ alone by God’s grace alone. So if the word ‘reward’ makes you uncomfortable, may be try replacing it with ‘gift’.
*all verses NIV2011