Most of the culture ships are named after punchlines to jokes about war, violence, and excessive use of force.
Part of the joke is that the culture partly abhors the use of violence but yet at the same time finds itself constantly engaged in acts of violence to protect itself and in the aid of those it feels morally required to aid.
Many of the warships have anti-war views, but believe in the necessity of some violence to achieve a greater good. Thus the culture feels the need to let off angst about war in different ways and the names of the ships is one of those ways.
"Of Course I Still Love You" for example, is a joke about how those who attack others are sometimes in abusive relationships, making excuses for their behavior. In this way the ship is joking about how the harm it inflicts on others is ultimately for the greater good of everyone, though it appears abusive.
Part of the reason that someone might name ships after culture ships, is the Culture is a utopia similar to Star Trek's Federation. In some ways representing a possible pinnacle of mankind.
Many of the ships are only named in passing, or are on the sidelines of a conflict, so many ships are not always important characters in a story. Both ships are from Player of Games and are friends with one of the drone main characters. I can't recall offhand if they had any significant interactions and I can't seem to find any detail about it online.