What is the genetic material called during prophase? and how do eukaryotic cells divide?

The genetic material is called chromatin during prophase.

Prophase is the first stage of mitosis. During prophase, the genetic material which is made up of DNA and proteins is called chromatin. Chromatin is found within the nucleus of cells and it condenses to form visible chromosomes.  

Eukaryotic cells (cells with true nucleus) divide through either mitosis or meiosis. Meiosis occurs in only sexually reproducing eukaryotes while mitosis is more common in all eukaryotic cells. Mitosis is the division of a cell nucleus in which the genome is copied and separated into two equal halves (daughter cells) while meiosis is the division of a diploid cell into four haploid cells, which develop to produce gametes.