Simon Finch was the first Finch to step foot on American soil. He made a great deal of money but was not happy so he got married. He had 8 daughters and one son. The son's name was "Welcome Finch." This is a clever little twist that Ms. Lee puts in the story. After 8 daughters a son was truely welcome in the Finch household, so they simply named him Welcome Finch. This part of the story can be found in chapter 9 on page 88, of "To Kill A Mockingbird."
Scout's great grandfather, Simon Finch, moved from England to avoid the persecution of Methodists. Eventually settling in Alabama, he became a self-made man, likely during the late 1800s, seeing as the events of the story, and Jem's childhood, take place during the 1930s. Simon built a wealthy homestead, called Finches Landing, on the Alabama River and started a family. For a man of means, you can imagine that it was disheartening to have no control over the gender of his children, as girl after girl was born. By the ninth baby, imagine the Finch's excitement to finally have a boy, whom they aptly (if uncommonly) named Welcome. During that time, the importance of producing a male heir was still quite prevalent, especially among wealthier families. Welcome seems to have received some special status as the only boy. For example, although his room was on the same floor as the girls', he had his own set of stairs, while the girls' rooms could only be reached through a stairwell in their parents' bedroom. Sadly, there wasn't much for Welcome to inherit, as the family lost all their wealth in the Civil War.