Are we talking about Azog here the one who killed Thorin Oakenshield's grandfather, Thrór? The same Thrór who after gotten kicked out as king under the mountain by the dragon Smaug, bequeathed one of the dwarf magic rings to his son Thráin II (Thorin Oakenshield's father). After losing the lonely mountain Thorin's grandfather decided to try to retake Moria. (A foolhardy task for there was still the balrog.)

Of course Thror died a bloody death, he was captured and tortured by Azog the Orc, the killed, and then his body was desecrated. Thror's death then caused a massive war between the orcs and the dwarves. In this war Thorin's father loses an eye and Thorin becomes a warrior and gains the title Oakenshield since his shield was destroyed Thorin just cut down a tree and used a branch to defend himself.

After many years of fighting Azog and his armies is defeated by the dwarves, Dain the II Ironfoot kills Azog after Azog kills Dain's father. Dain who is a cousin to Thorin aids Thorin with the dwarf army in the battle of the five armies. Dain also becomes king of the lonely mountain after Smaug and Thorin's death since Thorin left no heir.

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Thrain, Thorin's father, after gaining of the seven magic rings for the dwarves is encouraged by the ring for obtaining golds and riches (aka greed). Thrain is later captured by Sauron (in the "necromancer's tower" of southern mirkwood), is tortured by Sauron, and has his magic ring taken from him.

Gandalf later finds Thrain while doing research on the necromancer, Thrain gives Gandalf the map of the Lonely Mountain commanding Gandalf to give it to his son, but due to Gandalf not know who Thrain is and Thrain not able recall his son's name due to the ring driving him to madness and the torture of Sauron, made this task extremely difficult for Gandalf.

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Are we talking about the same Goblin here?