Germanium was discovered relatively late in the discovery of elements. It's existence and some properties were predicted by Dmitri Mendeleev by its position on his periodic table, dubbed Ekasilicon.
Clemens Wrinkler discovered it in 1889 at Freiberg University and named it after his home country of Germany. It was found in the mineral argyrodite alongside silver and sulfur. When Wrinkler analyized argyrodite he found that silver and sulfur only comprised about 94% of the mineral's total mass, he was eventually able to isolate the pure element and published his findings on February 6th of 1889.