I believe the term you're looking for is diagramless crossword. From Wikipedia:
In a diagramless crossword, often called a diagramless for short or, in the UK, a skeleton crossword or carte blanche, the grid offers overall dimensions, but the locations of most of the clue numbers and shaded squares are unspecified. A solver must deduce not only the answers to individual clues, but how to fit together partially built-up clumps of answers into larger clumps with properly-set shaded squares.
In its standard form, this puzzle consists of a loosely interlocking grid and a list of words to be filled in. You must use logic and elimination to figure out where to place the words. This category includes puzzles where the word list is clued rather than provided, but if the clues are associated with specific entries, this becomes a crossword puzzle instead.