As with many things in the novel, the title of "The Giver" can be interpreted with different meanings at different levels.
Because Jonas's assignment is to become the next Receiver of Memory for the community, it will become his duty to be a giver of advice to the elders of the community when they are faced with situations and decisions that require drawing on past experiences they can not remember.
As Jonas becomes aware of the superficiality of the existence of community members, he comes to believe that they need to be given their lost and hidden awarenesses in order to appreciate and more fully understand the beauties and hardships of life. Jonas plans to leave the community because he thinks those memories will be revealed to the community as a whole when he is no longer present to assume all responsibility for them. In this sense, he is acting as a giver to everyone.