The first Boswell's Circus was founded in 1882 by James Clements Boswell, the son of the clown and artist James Boswell (1826-1859). It closed in 1898. J. C. Boswell had five sons who were all artists, and the circus was revived in 1912 as Boswell's Royal Hippodrome and Circus Company. It later became known as Boswell Brother's Circus and Menagerie, and later again as just Boswell's Circus. The artist family of Boswell are not closely, if at all, related to the biographer James Boswell (1740-1795). You can read more about the circus and it's history here.
Pop singer Eve Boswell was born Eva Keleti in Budapest, Hungary in 1924. In 1939 she joined Boswell's circus (see above) as an artist. She fell in love with Trevor McIntosh, step-son to one of the owners of the circus, whom she later married. He also taught her English and suggested she change her name to Eve Boswell, after the circus. As is the case with the Boswell family who founded the circus, Eve Keleti Boswell is obviously not related to James Boswell, the biographer. You can read the story of her life in an obituary here.
The Boswell sisters
The Boswell sisters (the Bozzies) was a popular US harmony singing group active in the 1920s and 30s. It consisted of sisters Martha Boswell (1905-1958), Connie Boswell (1907-1976) and Helvetia Boswell (1911-1988), daughters of Alfred Clyde Boswell (1877-1944) and Meldania Foore (1870-1947). According to army records, A. C. Boswell was born in the US in 1877, and there appears to be no immediate connection between him (or his daughters) and James Boswell, the biographer. Read more about there Boswell Sisters here.
US Congressman Leonard Boswell was born 1934 in Missouri, the son of Melvin and Margaret Boswell. I have not been able to trace his ancestry any further at this time.
James Boswell (1906-1971)
The painter James Boswell (1906-1971) was born in New Zealand, the son of Scottish born schoolmaster Edward Blair Buchanan Boswell (1860-1933) and Ida Fair. Edward B. B. Boswell was born in Lanarkshire, son of James Boswell, who was born in Ormiston, East Lothian about 1832. James was the son of the caster Alexander Boswell and his wife Jane. Alexander's father seems to have been a James Boswell born ca. 1781. While the names James and Alexander runs in both the family of the biographer and of the painter, there is no evidence of any family relation between the two.
Who, then, is related to James Boswell?
The answer to part of that question can be found on the James Boswell desdendancy chart. You are welcome to ask questions about this, as well as other Boswell branches and descendants of James Boswell's ancestor in the forum.