I've tried this is pre2 and pre4, fails in both.
If I run a scoreboard command targeting players who have flint in their inventory with the Name of "TestFlint", it fails if that item has a stylized name (shown below). If I remove the color and italics, it seems to work fine. I've tried selecting by Name using the stylizing portions of the /give command as well, with no results.
# paste into command block
# indents shown here to help with code visibility
# does not work
give @p minecraft:flint{
display:{
Name:"{\"text\":\"TestFlint\",\"color\":\"blue\",\"italic\":true}"
}
} 1
# paste into command block
# indents shown here to help with code visibility
# works
give @p minecraft:flint{
display:{
Name:"{\"text\":\"TestFlint\"}"
}
} 1
# look for players holding TestFlint and increment their score
scoreboard players add @a[nbt={SelectedItem:{id:"minecraft:flint",Count:1b,tag:{display:{Name:"{\"text\":\"TestFlint\"}"}}}}] test 1
NBT has to match exactly, the value of Name is not without the ,\"color\":\"blue\",\"italic\”:true