Correct.

And he showed me a river of the water of life, clear as crystal, coming from the throne of God and of the Lamb, ²in the middle of its street. And on either side of the river was the tree of life, bearing twelve kinds of fruit, yielding its fruit every month; and the leaves of the tree were for the healing of the nations. ³And there shall no longer be any curse; and the throne of God and of the Lamb shall be in it, and His bond-servants shall serve Him; ⁴and they shall see His face, and His name shall be on their foreheads. Revelation 22:1-4 (NAS)

His name (the name of God and of the Lamb) was written on their foreheads.

This mark was described earlier in Revelation 14:

"...having His name and the name of His Father written on their foreheads."  Revelation 14:1 (NAS)

Do you wear the name of God and the Lamb...or someone or something else?

"No one can serve two masters; for either he will hate the one and love the other, or he will hold to one and despise the other. You cannot serve God and mammon."  Matthew 6:24  (NAS)

The Water of Life:

There are several scriptures that talk about this imagery of the water of life:

O LORD, the hope of Israel, all who forsake Thee will be put to shame. Those who turn away on earth will be written down, because they have forsaken the fountain of living water, even the LORD. Jeremiah 17:13 (NAS)

Jesus answered and said to her, "Everyone who drinks of this water (the water from the well) shall thirst again; ¹⁴but whoever drinks of the water that I shall give him shall never thirst; but the water that I shall give him shall become in him a well of water springing up to eternal life." John 4:13-14 (NAS)

"He who believes in Me, as the Scripture said, 'From his innermost being shall flow rivers of living water.'" ³⁹But this He spoke of the Spirit, whom those who believed in Him were to receive; for the Spirit was not yet given, because Jesus was not yet glorified. John 7:38-39 (NAS)

The Tree of Life:

The tree of life in the garden of Eden was the tree that provided eternal life to those who ate of it (see Genesis 3:22).  Proverbs 3:18 describes wisdom as a tree of life to those who take hold of her.  Proverbs 11:30 describes the fruit of the righteous as a tree of life. Other passages in Proverbs give other comparisons.

Eternal life is promised to those who are bond-servants of God and Christ.  Here are just a few of many scriptures:

"And everyone who has left houses or brothers or sisters or father or mother or children or farms for My name's sake, shall receive many times as much, and shall inherit eternal life. Matthew 19:29 (NAS)

"And these will go away into eternal punishment, but the righteous into eternal life." Matthew 25:46 (NAS)

"He who believes in the Son has eternal life; but he who does not obey the Son shall not see life, but the wrath of God abides on him." John 3:36 (NAS)

"Do not work for the food which perishes, but for the food which endures to eternal life, which the Son of Man shall give to you, for on Him the Father, even God, has set His seal." John 6:27 (NAS)

But now having been freed from sin and enslaved to God, you derive your benefit, resulting in sanctification, and the outcome, eternal life. Romans 6:22 (NAS)

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