What is the name of the theory opposite to the Great Man theory?

This is a completely intuitive answer - I would call it the tidal force interpretation of history. The great voyages of exploration did not acheive technological or political feasibility until many evolutionary steps, in ship-building, in the development of trading arrangements, in nation-building, in the conflicts arising all accreted to engender the conditions sufficient & necessary for such undertakings, with their manifestly portentous consequences, over the following centuries.

Now, reducing that long emerging historical process to the single inspiration of a Columbus or Magellan would be a caricature, historically speaking. That said, on the margins, individuals can have great effect - but the argument concerns the great tide of history, not its accidents, which are often enough provisional based upon current somewhat arbitrary conditions (say, the carving up of the Levant & Arabia post WWI). Was Balfour a great man, or simply the clerk in charge of drawing the lines empowered by the great powers, whose interests were bound to be represented, however haphazardly as turned out.

So I propose, in counter to the individualistically-centered Great Man theory of history, the Tidal Force (or Mass Effects or Emergent Process) theory of history.

There's an old historical saying......."Does the man make the times or do the times make the man?"

In our contemporary history and historiography, The (now dismissed and largely discredited), "Great Man Theory of History"-(originated by Thomas Carlyle), was, in a way, a reading and studying of History through a biographical-(almost Plutarchian) lens. That is to say, History, had been determined and impacted solely by "Great" historical figures, such as certain Generals, Statesmen, Inventors, Scientists, Artists, Religious Leaders and Philosophers. In a way, (despite the rabidly leftist history and historiography that has been produced over the past 25 plus years), Carlyle's (allegedly) anachronistic "Great Man" Theory may not be so implausible-(Of course, it all depends on how one defines, "Great". Alexander III of Macedon was and is still described as, "Great", whereas Ivan was and is still described as, "The Terrible". Even Attila is referred to as, "The Hun", which did not, nor does it exactly connote a complimentary meaning. So again, it all depends on how one defines, "Great" and /or "Greatness").

The opposite reading of Carlyle's "Great Man of History", would probably consist of 2 socio-historical schools of thought, very much to the left of center:

The older Marxist school-(which originally emanated from the earlier Hegelian school, though Hegel's Dialectics were quite distinct from Marxian Dialectics), has been one of the more popular approaches towards historical study, writing and research within the West since the mid 1960's-(and perhaps earlier).

The Marxist approach towards History is predicated on the idea of class struggle; a uniting of working peoples to determine the future outcome of society and civilization through a radical campaign of depersonalization and deindivdiualization, followed by the dissolution of the Corporate class and the State, as a way achieving the Greater and collective virtue of universal equality. In other words, people, not individuals, communities and not leaders, catalyze the historical, as well the unfolding of events.

The 2nd and more recent school of thought, is Post-Modernism, founded and popularized by the French Philosopher and Social Critic, Michele Foucault. Although Foucault wrote most of his major works during the 1960's, his intellectual legacy would come a generation or so later, better known as "Political Correctness". Michelle Foucault may not have been directly responsible for the onslaught of Political Correctness, unfortunately though, his writings were very influential.

The essence of Post-Modernism and indeed, Post-Modern thinking is that the concept of truth does not exist. That the traditionally defined properties and categories of knowledge are not universally provable, but instead, are of relative consequence. Therefore, there is no Objectivity, nor is there a meaningful search or exposition of evidence, because such a search and such an assumption do not exist.

With regard to historiography, Post-Modernism-(and its rabidly righteous twin, Political Correctness), has been the dominant and encompassing approach towards the research, writing and teaching of history at the secondary, college and graduate levels within the United States for the past 25 plus years. It is a philosophy and social movement that is to the left of Marxism!-(if one can imagine that).

However, both Marxist and Post-Modern historiographies, share one thing in common, a mutual contempt for individuality and a centralization-(even a romanticizing) of the collective and the group dynamic. For Marxists and Post-Modernists, individuals have never determined historical outcomes, it has always been progressed, advanced and determined by an activist populace and citizenry.

To the Marxists and Post-Modernists, NEITHER "the man makes the times, nor the times make the man", because man, that is to say, the individual is either, an elitist or the individual does not exist because the very notion of an individual is the product of a social construction. Either way, the loss of historical individuality has been central to both of these above mentioned movements..........(and they are winning to this day).

It's called "History from Below". I justify this by quoting Herbert Spencer:

You must admit that the genesis of a great man depends on the long series of complex influences which has produced the race in which he appears, and the social state into which that race has slowly grown.... Before he can remake his society, his society must make him.

-- Herbert Spencer, The Study of Sociology.

Spencer's position on this is typically associated with History from Below, aka People's History.

From Wikipedia:

A people's history, history from below, is a type of historical narrative which attempts to account for historical events from the perspective of common people rather than leaders.

There is an emphasis on disenfranchised, the oppressed, the poor, the nonconformists, and otherwise marginal groups. The authors are typically on the left and have a Marxist model in mind, as in the approach of the History Workshop movement in Britain in the 1960s.

I'm not sure Spencer was especially socialist, but the observation has been seized as a justification by those who are. Spencer's point, as I interpret it, is that "great" men are simply able men who happen to be ready when conditions are ripe; in the right place at the right time. They are artefacts of events rather than prime movers, and merely the first to move of several potential actors.

This is certainly the antithesis of the GM theory, and whoever put the reference to History from Below in the Wikipedia piece on GM theory clearly shares this opinion, so presumably takes a similar interpretation of Spencer.

Key to this perspective is the insight that we are not masters of our own destiny. We can choose how we react to circumstances but we cannot choose the circumstances themselves. We can try, but as every other person is also trying to control events it cancels out like the magnetic fields of micro-domains in iron; influence is strong locally but on a grander scale they come to nothing.

Not every thesis has a single antithesis or opposite. However, we can highlight a few trends or schools of thought in historiography (the study of history) that contrast most sharply with the Great Man Thesis.

One such answer is implicitly given in the question itself: historical sociology. The early sociologist Herbert Spencer directly critiqued the Great Man theory. A key theme that sociology, anthropology and other social sciences share with history is the question of structure versus agency. The Great Man Thesis is an approach which strongly emphasizes a specific form of agency, in contrast with more structural approaches.

Within the field of history itself, perhaps the most explicitly structural perspectives are that of the Annales School (for example see Fernand Braudel) and of Marxist historiography (for example see Eric Hobsbawm).

Another way to look at this question is that the Great Man thesis emphasizes the roles of heroes and leaders. In that sense, the opposite approaches are social history and "people's history". The work of E. P. Thompson is a good example here. He is definitely not a structuralist, but instead emphasizes the agency of the working class.