In Talmudic literature (Gemara Sanhedrin 56a) and Maimonides' work, the Mishneh Torah (Laws of Idolatry 2:7, Laws of Kings and Their Wars 9:3) and other works; the phrase "blessing the name" is used euphemistically to mean cursing the name of G-d.
In Sanhedrin 56a the Talmud describes the legal proceedings against a person who "blesses the name." During the trial the chief witness is asked to tell the court what was said using a euphemism "may Yosi strike Yosi." Once this is done the court is cleared and only the judges and the witnesses remain. The chief witness is asked to tell the court exactly what the person in question said without the euphemism, using instead the name of G-d. Once this is done the other witnesses will say "I too heard as him."
The penalty for "blessing the name of G-d" is a death penalty. In the case of the Jewish person they are executed by stoning. In the case of the non-Jew he is always executed through decapitation; which is considered a faster and less painful death than death by stoning.
The reason that the Noahide death penalty is decapitation in most cases is because the only place where death penalties are mentioned in relation to gentiles is Genesis 9:6. There we are told: "Whoever sheds the blood of man, by man shall his blood be shed..." meaning, we are told that in order for a person to be put to death their blood must be shed. The only death penalty mentioned in the Torah involving shedding blood is decapitation. The Torah describes other death penalties for Jews.
Very often the prohibition against "blessing" the name is confused with the prohibition in Exodus 20:7 against swearing falsely by G-d's name. Swearing falsely by G-d's name is much different but related to using G-d's name to "bless" him.