While the circle mark is commonly used in marking Japanese assignments, the lozenge shape doesn't have a standard usage. I've tried searching everywhere; I can't find a common meaning to the mark on homework (or even a single instance of a diamond mark being used on homework, for that matter)
Here are a few possibilities:
The teacher or school has created his / her own specialised usage for it eg. to mean "not bad", "needs more work", etc.
The teacher simply uses it to mean "good job" because it is aesthetically pleasing (perhaps the teacher really likes diamond shapes or diamonds, because stars are more common, I think)
If this is your own worksheet we are talking about then perhaps the only way to know is to ask the marker.
As for the name, as choco has already pointed out above, it's called 菱{ひし}形{がた}:
★ Diamond Shape, or Rhombus, in Japanese is 菱形 (ひしがた – hishigata).
★ Another word for Diamond Shape, or Rhombus, is 斜方形 (しゃほうけい – shahōkei)