There are 876 Reform congregations in North America, 499 of which have "Temple" in their names, so the formal name is pretty common and it's not unreasonable to think that people refer to the others as "temples" too. As noted by DoubleAA, the first (apparent) use of the name was the Hamburg synagogue in 1818. Documentation about naming practices that early is hard to come by, but we might find hints in the official "platforms" published by the Reform movement (as it formed into an actual movement).
The first of these, from 1885, explains their views on Zionism and messianism:
We recognize, in the modern era of universal culture of heart and intellect, the approaching of the realization of Israel's great Messianic hope for the establishment of the kingdom of truth, justice, and peace among all men. We consider ourselves no longer a nation, but a religious community, and therefore expect neither a return to Palestine, nor a sacrificial worship under the sons of Aaron, nor the restoration of any of the laws concerning the Jewish state. [...] We are convinced of the utmost necessity of preserving the historical identity with our great past.
Perhaps the combination of "we're not anticipating a third temple" and "historical identity is important" led to the name being considered appropriate. Nearly a century later, the 1976 platform said:
We are privileged to live in an extraordinary time, one in which a third Jewish commonwealth has been established in our people's ancient homeland. We are bound to that land and to the newly reborn State of Israel by innumerable religious and ethnic ties. [...] At the same time that we consider the State of Israel vital to the welfare of Judaism everywhere, we reaffirm the mandate of our tradition to create strong Jewish communities wherever we live. A genuine Jewish life is possible in any land, each community developing its own particular character and determining its Jewish responsibilities. The foundation of Jewish community life is the synagogue. It leads us beyond itself to cooperate with other Jews, to share their concerns, and to assume leadership in communal affairs.
The temple was the center of Jewish life in biblical times. The Reform movement does not seek a third temple but believes that such centers of life are necessary everywhere that Jews live, and also that maintaining a connection with our national history and land is important. One way to do that is to refer to those local centers as "temples".
