John W.'s name was Johann Weisbart Bockhorn. His father was Johann Hinrich Bockhorn but no details were given about the place in Germany where his father came from. John's mother was Rosina Elizabeth Siems. Later it turned out that she was a widow at that time of her marriage and that her maiden name was Weisbart. That was an explanation of John's unusual first name.
The only thing I found out about John's emigration to America was the departure with the ship "Isabella" from Bremen on 19 August 1835. He arrived New York on 01 October 1835. His naturalization took place in New York on 23 October 1839. New York was his chosen place of residence.
Why emigration from Bremen? An Atlantic passage from a German port was much more expensive than from an English port. I only can suppose the reason why. John's parents died young. His mother died on 11 June 1820 and his father John Hinrich on 13 May 1827. John was a child at this time and was probably sent to relatives in Germany. The parents are buried in the cemetery of St George's German Lutheran Church on Little Alie Street, Whitechapel.

Could the death of the parents have been a consequence of several cholera epidemics? Many people lost their lives.

The "Journal of the History of Medicine" wrote in January 1972:
There are 4,513 deaths listed in the mortuary books of St. Bride's Parish from 1820 to 1849, 2,338 (51.8%) of them male and 2,175 female. In complete years the deaths ranged from a low of 100 to highs of 224, 223, and 224 in 1831-33. Cholera was epidemic in parts of London in those years.

John's occupation was grocery clerk and he had his own shop in New York. He was also politically active. In 1861 he was an elected school inspector and in 1864 a councilman. In 1877 there was a court dispute about his former business. He had sold it before and the buyers were fighting with former shareholders of the disbursement.
There is unfortunately no information about John's wife. I know that she was a born Schaffer or Schäfer and that she was born in Bavaria or Hanover in 1825.I found news about John's father John Henry Bockhorn a large probability his original name Johann Hinrich Buckehorn. This family was called Buckehorn before 1800 and Buckhorn and Bockhorn after 1800. That's maybe the reason why John changed his name so many times.
John Hinrich Buckehorn was born in Heißenbüttel , municipality of Hambergen on 10 November 1783. Heißenbüttel is a village between Bremen and Bemerhafen. A lot of Bockhorns, Buckhorns and Buckehorns lived in this area. The father of Johann Hinrich was a Hinrich Buckehorn, who was born on 06 November 1758 in Wallhöfen, municipality of Hambergen. His mother was Gretje Wrieden. She was born in Heißenbüttel on 24 March 1760.
Clarification about the birth place of John Henry could only bring the death certification. The internet is far-reaching and I could download the death note contained in the church register of St George's. It was disappointing. No information about his birth or birth place. The only valuable information was his age as he died. He died at the age of 44 years making his birth year 1783. It was the same year as Johann Hinrich from Heißenbüttel was born. It is not clear evidence but I think the missing link was found.

There was also a George Bockhorn in London and later in New York. It was not possible to find out who he was. He doesn't appear in US or UK censuses. Maybe under a different name? The only information I found was the baptism of his daughter Rachel on 23 December 1820 in St Matthew, Bethnal Green, London. The name of the mother was also Rachel. Beside this is George also mentioned in the last will of Rosina Elizabeth Bockhorn, John Henry's wife.

The results also lead to John W. Buckhorn from Liverpool. He lived as borderer in the household of a Seefut family in 1861. A Bockhorn from Heise, municipality of Bramstedt, married a woman from a Seefuß family. Maybe this John W. Buckhorn also belongs to the Bockhorns from the Hambergen area in Germany.

Remark on the family Seefus:
The entry in the UK census is not very readable. It's possible that the family name "Seefus" was meant, what is more probable. The "Lancs OnLine Parish Clerks Project" reports about John Seefus, who lived in the Vauxhall Road in Liverpool and baptised a son in 1861.
The church register of St George in London tells about a Johann Seefus from Heise. He lived in 1849 and 1850 1 Princes St, 8 John St.
Every piece is one closer.

My friend Carolyn Day has always a surprise ready. She sent a newspaper clipping a couple of days ago (09.08.11). The newspaper clipping was taken from the London "Morning Chronical" (1769 - 1862) of 22 October 1840.
The original text reads as follows:

Messrs. Johanna, Seiler, and Bockhorn (late Weisbert and Siems) beg to announce they have commenced business at their original manufactory, No. 4, Old Castle-street, Whitechapel, as well as at No. 3 Sharp's-alley, West Smithfield, where may be obtained every description of violin and harp strings of the best quality, at the lowest prices.

Confusion pure! How could be Mrs Bockhorn a late Weisbert (Weisbart?) and Siems? The mother Rosina Elizabeth was a born Weisbart and widowed Siems. But she died in 1820. How did her name come into the newspaper of 1840? Why did they keep her first name secret? Was the newspaper also confused about the ladies? What other reason could have the comma between Johanna and Seiler?

The internet presentation of "FreeBMD" offers information about a Mary Elizabeth Bockhorn. She died in 1874 in Pancras, aged 70 year. The census of 1851 helps with information:

Address: 86, St John Street Road, Saint James Clerkenwell, Finsbury
County: Middlesex
Buckhorn, Mary, Head, Widow, female, 47 years old, born 1804, Share Holder, Whitechapel, Middlesex
Miller, Charlotte, Sister, unmarried, female, 30 years old, born 1821, Share Holder, Whitechapel, Middlesex

So was Mary Elizabeth a born Miller. But who was her late husband? And also here the names confusion.

The census of 1841 tells about Johanna Seiler:
Address: Old Castle Street, St Mary Whitechapel, Tower Hamlets
County: Middlesex
Seiler, Johanna, female, 56 years old, born 1785, Harp string maker, Middlesex
Siems, Margaret, female, 51 years old, born 1790, Middlesex
Siems, Margaret, female, 20 years old, born 1821, Middlesex

There was also a connection between the Siems and Seiler family.

There are still a lot of open questions. Do you know more? Contact me.

As usual was my good friend Carolyn Day a huge support in this research. She could contribute a lot of information and help. Thank you, Carolyn.