Targum Yonasan: The Beis ha'Mikdash and the land of the house of My Shechinah. Radak - this refers to [within] the houses of the Heichal, and the walls of the Azarah. Chachamim are there constantly, and they mention the deeds of the current and prior Chasidim.

Radak: It is a place, like "v'Yad Tihyeh Lecha" (Devarim 23:13).

Malbim: It is help in his house ¹ - something that a childless person lacks.

Radak: I will continue his name for generations - "Shem Olam Eten Lo Asher Lo Yikares." This is like Hashem told David "v'Asisi Lecha Shem k'Shem ha'Gedolim Asher ba'Aretz" (Divrei ha'Yamim I, 17:8). Even though a person's straight and good deeds perpetuate his name, when he is good in front of Elokim, and has good intent in his deeds, Hashem puts in people's hearts to mention him for good for all days; sons hear of his deeds from their fathers. This is part of his reward after death, aside from the great reward guarded for his Neshamah.

Malbim (4): Individual endurance [of the Nefesh] is better than continuity of the species. Individual continuity is via three things - Emunah, Mitzvos (deed) and learning Torah (investigation). Corresponding to these, the verses mentioned Shabbos, ba'Asher Chafatzti and Brisi.

Malbim: Continuity of the species lapses after the generation of his children. I will give to him an eternal good name.

Radak: I will give to each Saris. Many verses are like this.