The President's 13-year-old son hasn't actually taken possession of the small-breed Mongolian horse, which President Battulga Khaltmaa symbolically gifted last month.
But Battulga arrived eager to learn whether the animal had been named, according to a senior administration official.
It has, according to Trump: "Victory."
"Did you see a picture of the horse?" Trump asked reporters. "Beautiful."
The tiny breed is a symbol of the country, where they outnumber people. Genghis Khan was said to ride one. They've been given to visiting dignitaries before, including then-Defense Secretary Chuck Hagel.
The Trump administration hoped to send a message to Beijing and Moscow by inviting Mongolia's leader for talks at the White House.

The landlocked country's borders with Russia and China make it an ideal place for listening and strategic relations, a senior administration official said. The official claimed it is hard to envision a country better placed to develop US relations.
Officials said the visit would give the US leverage in the ongoing trade negotiations with China, the latest round of which wrapped this week. More than 90% of Mongolia's trade goes through China, the official said, and the US is looking to help Mongolia develop other options.
Cashmere was a main topic of discussion. Mongolia is one of the world's leading producers of cashmere and right now most of Mongolia's raw cashmere is sent to China, where it is made into products and exported. Alternatives to that process could be created -- Mongolia could develop the wool itself, with the help of the US, and export it in a way that would more economically favor Mongolians.
The leaders were also expected to discuss a number of other topics, including military cooperation between the US and Mongolia and investment in Mongolian minerals.
It was the first visit of a Mongolian president to the US since 2011. The Trump administration sees Mongolia as having been long neglected by the US. Now, the administration is tending to the relationship, the official said.