The phrase "sanctification of the Name" does not occur in the Hebrew Bible, but the instruction "To sanctify His Name" and conversely "And ye shall not profane My holy name" (Lev. 22:32) is frequently expressed. Any action by a Jew that brings honor, respect, and glory to God is considered to be sanctification of his name. In contrast, any behavior or action that disgraces, harms or shames God's name and his Torah is regarded as a chillul Hashem (desecration of the Name).
Martyrdom during the Hadrianic persecution is called sanctification of the Name in Bavli Berachot 20a and Midrash Tehillim. The ultimate act of sanctification of the Name is a Jew who is prepared to sacrifice his life rather than transgress any of God’s three cardinal laws: banning serving idols (Avodah Zarah, or foreign worship), committing certain sexual acts (such as incest or adultery) or committing murder. The commandment was introduced by the Exegetes 
The Jews who were executed or exiled from Spain and Portugal by the Spanish or Portuguese Inquisition because they did not renounce their religion are called kedoshim (holy ones), because they are regarded as having fulfilled the commandment of not turning to idolatry and thereby sanctifying God's name.
Another way to be categorized kedoshim is to be killed for being Jewish, even if one is not given the opportunity to convert or otherwise disassociate with the Jewish faith. Thus, the Jews who were killed during the Holocaust because they were Jews are considered kedoshim.
- Marvin Bash Messages of the Chofetz Chaim: 100 Stories and Parables 2006 Page 91 "Section VII Sanctification of the Name: An Introduction It is written in the Torah, as one of the commandments, “You shall be holy, for I am holy” (Lev. 19:2). According to this Biblical verse, the Jew is obligated to be holy, ..."
- Esther Marie Menn Judah and Tamar (Genesis 38) in ancient Jewish exegesis 1997 p. 262 "The Hebrew Bible itself, however, does not employ the phrase "sanctification of the Name" to describe this type of positive connection.... "Sanctification of the Name" in the teachings of the tannaim 44 (1979) 28-42.
- Craig A. Evans, James A. Sanders The function of scripture in early Jewish and Christian tradition 1998- Page 218 "R. 2.7, in which the words 'Give your soul for the sanctification of the Name'.... Martyrdom during the Hadrianic persecution is also called 'sanctification of the Name' in b. Ber. 20a and Midr. Teh.
- "Jewish Virtual Library".
- Safrai, Samuel (1979). "קידוש השם בתורתם של התנאים [Sanctification of the Name in the Teachings of the Exegetes]". ציון [Zion]. 44, pp. 28-42. [Hebrew].