'Servant's' in the Bible

And he said, “See here, my lords, please turn aside and come into your servant’s house, and spend the night, and wash your feet; then you may get up early and go on your way.” But they said, “No, we shall spend the night in the open plaza [of the city].”

Yet this was very insignificant in Your eyes, O Lord God, for You have spoken also of Your servant’s house (royal dynasty) in the distant future. And this is the law and custom of man, O Lord God.

However, I will not tear away all the kingdom; I will give one tribe (Judah) to your son for the sake of My servant David and for the sake of Jerusalem which I have chosen.”

However, I will not take the entire kingdom out of his hand; but I will make him ruler all the days of his life for the sake of My servant David, whom I chose because he kept My commandments and My statutes.

Yet for the sake of His servant David the Lord was not willing to destroy Judah, since He had promised to give him a lamp (enthroned descendant) through his sons always.

This was a small thing in Your eyes, O God; but You have spoken of Your servant’s house for a great while to come, and have regarded me according to the standard and estate of a man of high degree (prominence), O Lord God.

O Lord, for Your servant’s sake, and in accordance with Your own heart, You have accomplished all this greatness, to make known all these great things.