When the expression "the name of the father" first appeared in Lacan’s work, in the early 1950s, it is without capital letters and refers generally to the "prohibitive role" of the "symbolic father" as the one who lays down the incest taboo in the Oedipus complex.
Legislative and Prohibitive Function
The rexpression is at once a semi-humorous religious allusion (In nomine patris) and a play on the near-homonyms non and nom: the name-of-the-father (le nom du père) is also the father's "no" (le "non" du père) to the child's incestuous desire for its mother.
From the beginning Lacan plays on the homophony of le nom du père (the name of the father) and le 'non' du père (the "no" of the father), to emphasize the legislative and prohibitive function of the symbolic father.
A few years later, in the seminar on the psychoses, the expression becomes capitalized and hyphenated and takes on a more precise meaning; the Name-of-the-Father is now the master signifier which permits signification to proceed normally.