The "Mormons" were never given a state or made a state. The Mormons suggested a state called Deseret, but it was denied and was never made a state. The state of Utah became a state in 1896 during the administration of Grover Cleveland. The boundaries were drawn by the federal government and the name was chosen by the government as well. The population of the state was mostly Mormon, but there was a sizeable population of other religious groups as well. So, Grover Cleveland gave statehood to Utah, not to Mormons. Most Mormons at the time lived within Utah, but they did not choose the boundaries or the name.
Four legacies? Utah itself if the legacy!
Brigham Young University is named for Brigham Young, the second president of the Church of Jesus Christ of Latter-day Saints. He lead the Mormons to Utah. Education was always important to him, and he encouraged Mormons to get as much education as they could. He believed that there needed to be a university or an institution that gave a secular and religious knowledge to those in Utah, and it was Brigham Young who commissioned the start of the school.
The Mormons had a penchant for using biblical place names. Not only Zion, but also Moab, Goshen, Jordan River, Mt. Carmel. Looking outside Utah, the Strangite Mormons who settled Beaver Island, Michigan gave it Lake Geneserath, Mt. Pisgah, and another Jordan River.
Nearly everything in Utah was named by the Mormon pioneers - because they were the first people to settle there and discover these things!
Deseret from the Book of Mormon meaning honeybee.
Obviously it's because the Mormons traveled the trail.
Brigham Young did not start any religions. He was the second leader of the Church of Jesus Christ of Latter-day Saints (the "Mormon" church) which was founded by Joseph Smith, Jr. He led the Mormons from Illinois to Utah after Joseph Smith was murdered.
No. The Church of Latter-Day Saints officially banned polygamy in the 1800's when the concept created much debate among the Mormons (another name for those who are affiliated with the Church of Latter Day Saints). However despite this ban many Mormons practice polygamy still. In Utah, about 60,000 Mormons practice polygamy (5% of the Utah Mormon population).
Usually, nothing. For a brief period before Utah was a state, some saints referred to the settlements of non-Mormons as "Gentile". This practice lasted only a couple decades at most, as non-Mormons quickly began moving into predominantly Mormon settlements and inter-mixing with them.
Members of the Church of Jesus Christ of Latter-day Saints (the "Mormon" church) did not give Utah it's name. They wanted the state to be called "Deseret", but the United States government chose to call it "Utah" after the Ute Indians instead. Legend has it that the Mormons were okay with that name because "Utah" in Ute means 'top of the mountains', and Mormons believe that them settling in the area was a fulfillment of Isaiah's prophesy that "it shall come to pass in the last days, [that] the mountain of the LORD'S house shall be established in the top of the mountains" (Isaiah 2:2)
About 15% of the members of the Church of Jesus Christ of Latter-day Saints (the "Mormon" church) live in Utah (2 million Mormons in Utah and 15 million Mormons total). All Mormons, regardless of where they live, believe in the same religious commandments and moral guidelines. Mormons follow the Ten Commandments found in the Old Testament: worship God only, no lying, no adultry (sex outside of marriage), no murder, no stealing, no coveting, honoring parents, keep Sabbath day, do not take Lord's name in vain. They also follow the "Word of Wisdom" which is a health code prohibiting the consumption of alcohol, coffee, tea, tobacco, and illegal drugs. Mormons also follow guidelines which outline appropriate dress, dating relationships, and other moral standards.