Question: What emperor used the name between 1804 and 1813?
About the article "Vietnam", section "Etymology".

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The Danes took "Manly" into service, retaining her name and armament.
They commissioned her under Captain Holm but sold her on 28 October 1813. 
The name "Việt Nam" () is a variation of "Nam Việt" (; literally "Southern Việt"), a name that can be traced back to the Triệu Dynasty of the 2nd century BC.
The word "Việt" originated as a shortened form of Bách Việt (), a word applied to a group of peoples then living in southern China and Vietnam.
The form "Vietnam" () is first recorded in the 16th-century oracular poem "Sấm Trạng Trình".
The name has also been found on 12 steles carved in the 16th and 17th centuries, including one at Bao Lam Pagoda in Haiphong that dates to 1558.
Between 1804 and 1813, the name was used officially by Emperor Gia Long.
It was revived in the early 20th century by Phan Bội Châu's "History of the Loss of Vietnam", and later by the Vietnamese Nationalist Party.
The country was usually called Annam until 1945, when both the imperial government in Huế and the Viet Minh government in Hanoi adopted "Việt Nam".
Since the use of Chinese characters was discontinued in 1918, the alphabetic spelling of Vietnam is official.
The siege of Ganja and storming its citadel (November 22, 1803 - January 15, 1804), was a part of Russo-Persian War (1804–1813). 
The word "" originated as a shortened form of Bách Việt (), a group of ancient peoples who lived in what is now southern China and northern Vietnam.
This term first appears in the encyclopedia "Lüshi Chunqiu", compiled around 239 BC.
The character 越 may be read as ; Early Middle Chinese: "wuat"; literally: "more".
In 207 BC, Triệu Đà founded the Triệu Dynasty in Panyu (modern Guangzhou) and named his kingdom "Nam Viet" ().
This kingdom was "southern" in the sense that it was located south of other Bách Việt kingdoms such as Minyue, which was located in modern Fujian.
Several later Vietnamese dynasties followed this nomenclature even after these more northern peoples were absorbed into China and this original meaning forgotten.
In "Sấm Trạng Trình" (The Prophecies of Trạng Trình), poet Nguyen Binh Khiêm (1491–1585) reversed the traditional order of the syllables and put the name in its modern form: "Vietnam is being created" ().
At this time, the country was divided between the Trịnh lords of Hanoi and the Nguyễn lords of Huế.
By combining several existing names, Nam Việt, Annam (Pacified South), Đại Việt (Great Việt), and "Nam quốc" (southern nation), Khiêm could create a new name that referred to an aspirational unified state.
The word "nam" no longer implies Southern Việt, but rather that Vietnam is "the South" in contrast to China, "the North".
This explanation is implied by Lý Thường Kiệt in the poem "Nam quốc sơn hà" (1077): "Over the mountains and rivers of the South, reigns the emperor of the South."
Researcher Nguyễn Phúc Giác Hải found the word "Việt Nam" on 12 steles carved in the 16th and 17th centuries, including one at Bảo Lâm Pagoda, Haiphong (1558).
Nguyễn Phúc Chu (1675–1725) used the word in a poem: "This is the most dangerous mountain in Vietnam" ().
It was used as an official name by Emperor Gia Long in 1804-1813.</ref>The use of "Vietnam" was revived in modern times by nationalists including Phan Bội Châu, whose book "Việt Nam vong quốc sử" (History of the Loss of Vietnam) was published in 1906.
Chau also founded the Việt Nam Quang Phục Hội (Vietnam Restoration League) in 1912.
However, the general public continued to use Annam and the name "Vietnam" remained virtually unknown until the Yên Bái mutiny of 1930, organized by the Việt Nam Quốc Dân Đảng (Vietnamese Nationalist Party).
By the early 1940s, the use of "Việt Nam" was widespread.
It appeared in the name of Ho Chi Minh's Viet Nam Doc Lap Dong Minh Hoi (Viet Minh), founded 1941, and was even used by the governor of French Indochina in 1942.
The name "Vietnam" has been official since 1945.
It was adopted in June by Bảo Đại's imperial government in Huế, and in September by Ho's rival communist government in Hanoi. 
"Santa Margarita" was on the Irish station in 1804, followed by a period in the Channel between 1804 and 1807 under Captain Wilson Rathbone.
She was re-coppered at Plymouth in 1805 and again in 1806, and laid up in ordinary there between 1812 and 1813.