One common theme is the exploration of Katniss' internal struggle. Since in the original she was so focused on survival, fanfiction often shows how she deals with her love for Peeta while still trying to stay alive. Another theme is the re - imagining of key moments. For instance, the way she volunteered for the Hunger Games might be retold with her love for Peeta as a motivating factor. Also, the theme of sacrifice is common. Katniss might be portrayed as being more willing to sacrifice for Peeta because of her love.
Well, a frequent theme is the hidden nature of Katniss' love. In these fanfictions, it's often about how she hid her true feelings from Peeta and others. There's also the theme of redemption. Maybe Katniss feels she needs to redeem herself for not being more open about her love earlier. Additionally, the theme of growth through love is common. As she realizes and accepts her love for Peeta, she might grow as a person, becoming more empathetic and less guarded. This can be shown through various scenarios, like how she interacts with the other characters in the districts after admitting her love.