visual - Another new puzzle type needs a name

_{For an example of how this type of puzzle works, see here...}

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I believe I have invented another new type of puzzle...

What is its name?

^{Colour-blind-friendly version available here.}

Begin by solving the 9x9 sudoku; each of the digits 1-9 must appear exactly once in each row, column and thick-bordered 3x3 box. Then apply some grid-deduction-deduction (!) and discover its name!

Hint:

Its name is 8 letters long. Though you may be able to guess it, you'll need to explain how to derive it from the puzzle...

Answer

The name of this puzzle is

Yajidoku

I solved the Sudoku, then learned from the other answers here, that the next step is to solve a Yajilin, a puzzle type I haven't heard of before. As these both steps are already covered in the other answers, I only give the combined solution here:

Now the last step is

to sum up in each of the nine Sudoku blocks both the numbers colored initially and the numbers blackend for the Yajilin. The middle block has no such numbers, the other sums are, read clockwise (like the arrows indicate) starting top left*:
25, 1, 10, 9, 4, 15, 11, 21
mapping this on 1-26 = a-z gives:
YAJIDOKU

*Addition:

If we order the colours as they appear in the rainbow from the outside to the inside, we have red - yellow - green - blue, which hints to start reading top left.