As you get to know the Old Testament you realise there is so much in those names. In particular it is fascinating that there are women mentioned in there. That was very unusual in a Jewish genealogy, and even more unusual when you realise who these women were. There is Tamar (v3) who tricked her father-in-law in to having sex with her so she could have a child, Rahab (v5) who was a prostitute, Ruth (v5) who was a Gentile, Bathsheba (v6) who committed adultery with David, and Mary (v16) who became pregnant whilst engaged to Joseph. As the ESV study Bible puts it "The lineage is comprised of men, women, adulterers, prostitutes, heroes and Gentiles - and Jesus will be saviour of all".
Why not follow the links above to read the stories of these women, and reflect that whoever you are and whatever you've done, Jesus came to be your saviour too.