Trademark issues regarding religion typically arise when dissidents of a religion splinter off, sometimes claiming to embody the "real" tenets of the original religion. A dispute then arises as to whether the offshoot can use the religion's name. According to the Dear RIch staff, that's what happened in both cases you cited.
Mary Baker Eddy founded Christian Science in 1866, and then in 1889 established the Church of Christ, Scientist. A group of followers later split off and founded their own church, the Independent Christian Science Church of Plainfield. A dispute arose as to who had the right to use the term CHRISTIAN SCIENCE. In 1987, the New Jersey Supreme Court ruled (Christian Science Board v. Evans) that CHRISTIAN SCIENCE was generic because the term and underlying precepts of Christian Science preceded the religious organization by 23 years and should therefore be free for all to use. (As one commentator noted, it was an odd point for the court to base its decision on, since most religious principles precede the resulting organization.) However, the name of the church -- Church of Christ, Scientist -- was not generic and was protectable. In a subsequent California case, decided in 2000 (Christian Scientist Board v. Robinson), a federal court made a contradictory ruling when it refused to find the term CHRISTIAN SCIENCE to be generic and ruled that two entities might coexist and claim rights if additional wording is added to avoid confusion -- for example, the Indepenent Christian Science Church. In any case the church founded by Mary Baker Eddy and the Christian Science Publishing Company have acquired additional trademark registrations, including several for the term CHRISTIAN SCIENCE.
The Seventh Day Adventist case, decided in 2000 (Stocker v. General Conference Corporation of Seventh-day Adventists), was a decision by the Trademark Trial and Appeal Board (TTAB). The TTAB ruled that since the Seventh-day Adventists had been using the trademark on its publications for over 130 years, the term was not generic and the church was entitled to maintain trademark rights.
As you may have realized, there are two tricky aspects to the application of trademark principles to religion. One is that the government is prohibited under the establishment clause of the Constitution from getting involved in the "establishment" of religion. So, in order to apply trademark law, the courts must not rule on which religion best expresses the virtues of its founder -- whether that means deciding which Sufi founded a sect, or which church best presents the views of Mary Baker Eddy. The second concern is that trademarks are signifiers for products or service in commerce and it is sometimes difficult to apply these "corporate" principles to religious entities.
The Dear Rich staff reports that you can learn everything you ever wanted to know about trademarks and religion by downloading this law review article, or by reviewing the entry on trademarks and religion in The Encyclopedia of American Civil Liberties, an excellent resource for all things that seem unfair.
P.S. This blog has again been reprimanded for permitting the use of "trademark" as a verb (see question above). As it is painful for us to receive such reprimands, please be advised that if you use "trademark" improperly in the future, we will be required to correct your question before publishing it.