Usually, the Trump administration referred to the virus as "coronavirus", "the coronavirus", or, more commonly in press releases and official documents, the official WHO name of "COVID-19". The response team headed by VP Mike Pence was termed the "Coronavirus Task Force", for example.
There are however, instances prior to March 12th, when the allegations were tweeted by a Chinese official for the first time, where a location was attached to the disease.
As far back as the start of February, White House chief economic advisor Larry Kudlow described the virus as "the Chinese virus" in an interview with Fox Business Network.
Mike Pompeo and Republican Senators & Representatives repeatedly used the term "Wuhan Virus" in press briefings and in debates in the weeks leading up to the 12th. On the 9th, GOP Leader Kevin McCarthy tweeted a link to the CDC website, saying that it offered "Everything you need to know about the Chinese coronavirus".
On March 10th, Trump retweeted a tweet by Charlie Kirk, the founder of Turning Point USA, which calls the virus "China Virus" and says that "the US stands a chance if we can control of our borders"(sic). In his address on March 11th which announced the travel ban to Schengen countries, Trump described the disease as a "foreign virus".
It should be noted that this is not specific to the Trump administration, indeed, before March, many media outlets also included a geographic adjective in their reporting, including the BBC, the Guardian, Al Jazeera, the Financial Times, Reuters, Scientific American, the Associated Press, the Global Times, and the Washington Post, amongst others. This term then fell out of use towards the end of February, as this analysis by Axios shows, being replaced by the WHO sanctioned terms.
In conclusion, then, while US administration officials usually used the term "coronavirus", or the medical term "COVID-19", there was significant use of a geographic adjective, be that "China", "Chinese", or "Wuhan". While this was not initially exclusive to conservative politicians or administration officials, in the last couple of weeks in response to many claims that the term is racist, offensive, and inaccurate, this language has become far less popular, and now is used in the US almost solely by Republican officials & conservative media outlets, and has become far more frequently used by these individuals.