One the highest aspiration for the a Jew (and a Noahide) is to make a kiddush HaShem, a sactification of the Name. While this is often associated with martyrdom, a kiddush HaShem simply refers to any act which brings the Name of G-d honour or respect. "For I will proclaim the name of the LORD; ascribe ye greatness unto our God" (Deut. 32:10). In contrast, the complete opposite is a hillul HaShem (G-d forbid), desecration of G-d's name, for which the capital punishment can be incurred. Leviticus 24:10-17 relates the incident of a Jew who violated the injunction of Exodus 22:27 and blasphemed in anger, and the Divine edict proclaiming this to be a capital offense. Moreover, it states there "ish ish (any man) who curses his G-d shall bear his sin." Why the double expression of ish ish (literally: a man, a man)? To include all mankind, Jews and Gentiles.
One must acknowledge G-d's presence constantly, must fear and love His holy name. "O give thanks unto the LORD, call upon His name; make known His doings among the peoples. Sing unto Him, sing praises unto Him; speak ye of all His marvellous works. Glory ye in His holy name; let the heart of them rejoice that seek the LORD. Seek ye the LORD and His strength; seek His face continually. Remember His marvellous works that He hath done, His wonders, and the judgments of His mouth" (Psalm 105:1-5) For every single occurence in life, we must thank G-d, for the sweet edicts as well as the harsh and accept them all with love and a subjugated heart. It is every person's duty to glorify G-d's name and to teach everyone who is willing to listen about His Awesomeness. Israel is called on especially to tell the nations about G-d's miraculous salvations and to spread the Truth of the Torah.
While Jews and Gentiles alike must praise HaShem, we are forbidden to even mention the name of foreign deities. "And the name of another deity you shall not invoke it should not be heard in your mouth." (Ex. 23:13) By mentionning foreign gods, one gives them a misplaced sense of respect and makes them deserving of reverence while nothing could be farther from the truth. In fact, Judaism prohibits all forms of mockery, except from mockery of idol worship. Mockery and idolatry negate each other since idolatry elevates the profane and gives in divine status while mockery makes a serious subject seem light in the eyes of others. For that reason, Jews refer the gods of the nations with contempt or disdain, by names like Yoshke'le, Krishka. By invoking the names of false gods, one gives power to the sitra achra, to the Dark Side, and strengthens evil in the world.
Respecting G-d also means studying the Torah. Noahides must study, not in the same way as Jews li'shma, for its own sake, but rather to understand the laws and obligations incumbent upon them and to be able to uproot false ideas or philosophies that they took on while in the worship of idols. In the same way, G-d bestows His wisdom to flesh and blood and therefore it is a mitzvah to honour Torah scholars and rabbis, and to rise before them. "Rabbi Yosi used to say: He who honors the Torah is himself honored by mankind. He who dishonors the Torah shall himself be dishonored by mankind." (Ethics of the Fathers 8:4) By living according to the Torah, one is worthy of having G-d's spirit dwell on him and it is proper to respect him.
"O praise the LORD, all ye nations; laud Him, all ye peoples. For His mercy is great toward us; and the truth of the LORD endureth for ever. Hallelujah!" (Psalm 117)