First off, I didn't come up with ALL of these names. Some, I found from Google, Greek Names, or other Fan Fictions. So, these are very creative names. And most of them have something to do with the District they are from.
District 1: Luxury
The kids from 1 are always named after something shiny or valuable. For example, Jewel. Jewel is valuable and shiny. So, I suggest naming your tributes from 1 after something valuable or shiny.
District 2: Masonry
Kids from District 2 are mainly named after kinds of masonry. For example, Mason. Mason is a type of stone.
District 3: Technology
Kids from 3 are usually named after electrical related words. For example, Wire or Techa.
District 4: Fishing
Kids from 4 are usually named after the Ocean, Fish, or Seashells. I suggest naming your tributes from 4 after Oceans, Fish, Shells, or even Greek Goddesses of the Seas.
District 5: Power
District 5 is sort of hard because it was never talked about in the book. The kids from 5 are usually named after words related to "Power." Such as Spark or Watt.
District 6: Transportation
Kids from 6 are mainly named after car brands. For example, Mercedes or Cooper.
District 7: Lumber
The kids from District 7 are mainly named after Trees, Wood, Axes, etc. For example, Axel, Barker, or Ava.
District 8: Textiles
District 8 is a little hard since there haven't been many characters from 8. Kids from 8 are usually named after Textile-Related words. For example, Lacey or Flax.
District 9: Grain
Kids from this district are always named after kinds of grain. For example, Rye, Bailey, or Barley. Some of those are kinds of grain they would grow in 9.
District 10: Livestock
Kids from 10 are sometimes named after oxen or cows. For example, Oxford or Melanie.
District 11: Agriculture
Kids from 11 are always named after something they grow there. Such as Soya, Pepper, or Willow. Those are some foods that they grow in 11.
District 12: Mining
And finally, is District 12. Kids from this poor district are usually named after flowers or coal. For example, Violet or Cole.
You can always look on Wikipedia or search Google for Tribute Names. Typing in "Greek Names" or "Greek Gods or Goddesses" will always come in handy. Hope this helped you!