His relationship to Beatrice is immediately established as one of a familiarity. If Beatrice had just referred to Benedick by his real name, than the audience would have no understanding of the level of knowledge they have of each other. This nickname lets us know that they not only know one another, but that there is some history invovled between the two. The first scene between the two of them will develop this back history further, by letting the audience know that Beatrice "knows Benedick of old." They could be old friends (their teasing is still too light to suggest they are enemies) or - as we learn later - a former romantic couple.