ULAANBAATAR, Mongolia — On his first international trip since being confirmed as defense secretary, Mark T. Esper has tried to affirm the United States’ commitment to its Asia-Pacific allies by sitting down with government leaders, taking in national landmarks and holding forth about “enduring bonds” and “deep friendship.”

In Mongolia on Thursday, he named a horse.

The 7-year-old brown horse was a gift from his Mongolian counterpart, bestowed as Mr. Esper briefly visited a country that is a fortuitous arena where the United States can assert itself in its effort to beat back what the defense secretary earlier called Chinese “tentacles” and Russian influence.

The visit was the third to Mongolia by an American defense secretary. It was also the third time a defense secretary has named a horse in this landlocked country of nomadic plains.

If Mongolian horse-naming is a barometer for anything, then maybe Mr. Esper’s decision to call his horse Marshall, after Gen. George C. Marshall, reflects Washington’s renewed focus on projecting more influence — both militarily and diplomatically — on the borders of both China and Russia, which Mongolia is wedged between.