Why is the billboard not introduced as such but as the eyes of Dr. T. J. Eckleburg?

The billboard—an advertisement for Dr. T. J. Eckleburg, an optometrist—is an important symbol in The Great Gatsby. Primarily, it symbolizes the eyes of God, who, as George Wilson says later on in the story, sees everything. This "God's-eye perspective" transcends the materialistic world represented by the billboard. It looks down, both literally and figuratively, on the denizens of the Valley of Ashes and those who regularly pass through, such as Jay Gatsby and the Buchanans, and their ceaseless desire for riches and social status.
If the billboard were presented as primarily a piece of advertising, then it wouldn't be able to provide such a perspective, for it too would be a part of that shallow, materialistic world. It needs to remain above the fray to maintain its full force as a symbol. To that end, it's telling that the billboard is old and tatty, making the eyes of Dr. Eckleburg more prominent amid all the faded lettering. The symbolism is hard to avoid. The material things of this world will eventually fade away and die, but God—as represented by the eyes of Dr. Eckleburg—is eternal and will always see everything.