From the New Pauly:

This function was held, in Ptolemaic and Roman Egypt for example, by the agoranómoi , and in the Roman Imperial period and especially in Late Antiquity, the tabellio (documentary scribe).

It then goes on to talk about how notarius is not actually a notary but is a late antique term for a particular kind of imperial administrator.

Rome during the Principate and the late Republic did not have a centralized bureaucracy, simply because of the way the government worked. Citizens were elected to serve public magistracies, of which there were a fairly limited number--besides quaestors, praetors, consuls, etc. there were only a fairly small number of minor magistracies, and the major ones fulfilled most of the functions that we would expect a bureaucracy to fill now. Low-level administrative work, of the sort that bureaucrats employed by the state do now, was done mainly by the slaves, freedmen, household, and friends of the magistrate under whose auspices the work fell--magistrates also frequently hired out professional scribes and so forth as third-party help. The New Pauly notes that under the late Republic and early Principate these professional scribes were often slaves or freedmen (this includes those who actually were part of a magistrate's household--they would've been trained for this work and were no less professional), who drew up both public and private documents and served as witness to them as well. Under the later imperial structure these professional scribes became increasingly subject to centralized control (although it was not until Justinian that they were organized in a guild with an imperially-appointed guildmaster overseeing them). Even during the late empire, however, professional scribes still took care of both state business and private documentation (especially contracts and wills)--their stations could be easily found in and around the forum