The name Clara comes from latin word clarus, which means clear or bright and that is the exact thing, what means Clara for the Doctor.
This is from fanfiction I’m working on: 'Clara, my Clara.' He whispered. He liked the taste of her name on his lips. His always bright and shining Clara, the light in his darkness, like the ancient light of Pharos, navigating sailors through the dangerous reefs. She’s got dark sides too, like the lighthouse moves it’s light and makes shadow, but she was very very dear to him, the closest person he had. He needed her. He needed her to say to him, that he is doing good, that he hadn’t turned to evil, because it was so hard now, to recognize what is good and what is bad. It shouldn’t be but it was. He had lived a long life and had so many memories, all mixed up together. It was like to have voices in his head screaming over each other, he almost had headache. But she always quiet them.