There were many with the surname Bruce, but Robert was THE Bruce.
Robert 1 of Scotland is known as Robert the Bruce primarily because he is so much the national hero, and he was the only Bruce king.
Edward 1 of England had most of Roberts family killed, and he captured and imprisoned all the rest except for one brother, who had no legitimate children.
When Edward 2 finally freed his remaining family members after 6 (?) years of imprisonment in sometimes extremely harsh conditions, his wife was unable to have more children.
Robert’s only daughter married the son of the High Steward of Scotland, and the crown passed to the Stewart family.