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int colIndex = this.grid.Binder.NameToColIndex("SomeName");
If I understand your question about coloring only the header to the right of the visible grid, then I do not know of any grid properties that would help you here.
If you want to color the whole area, try setting grid.Properties.BackgroundColor. Another thing to try would be to set grid.HScrollPixel = true to see if this will hide the problem (with this setting you should not see any space to the right unless there are not enough columns to fill the clentwidth in the first place.)
If you want try to put up a fake header, you could put up a panel the height of the header row, and try to dock it so it will stick at the top of the grid. This would likely take some trial and error.