How to achieve this type of table layout in libreoffice and what's it's called?

Perhaps you mean Merging and Splitting Cells

It is simply called a table with merged cells.

You start with a 3-row×7-column table. You merge vertically the first two rows for cells in columns 1, 2, 3 and 7. You merge horizontally cells in first row, columns 4-6.

When you ask here, always mention OS name, LO version and save format. The latter is the most important since most recipes are only valid for .odt.