This new puzzle type needs a name {6}

I believe I have invented** a new type of puzzle…

What is its name?

Begin by solving the Fillomino puzzle:

Rules of Fillomino (adapted from Nikoli)

• Fill in all empty cells with numbers under the following rules.
• Numbers should be grouped together into ‘blocks’ of orthogonally connected cells in which each cell contains the same number.
• The total number of cells making up each ‘block’ equals the value they all share (e.g. a block of two 2’s, three 3’s, etc.).
• Different ‘blocks’ of the same size and value cannot border each other, horizontally or vertically (but may touch at a corner).

Then apply some grid-deduction-deduction (!) and discover its name! Answers which explain the deduction process are appreciated even more – thanks!

_{** NB After creating this puzzle, I realised that @Reinier has created something with similar inspiration before, but I believe our two puzzles are sufficiently different… Try to resist peeking at their puzzle before solving this one! 🙂}

^{Other puzzles in the ‘This new puzzle type needs a name’ theme: 01, 02, 03, 04, 05}