I have found pictures from another occasion, and we can see that the bracelet bears the names of both Beatrice and Eugenie!
Sarah Ferguson, Duchess of York, attends Annual Charity Day Hosted by Cantor Fitzgerald and BGC at BGC Partners, INC on September 11, 2014 in New York City. (Sept. 10, 2014 - Source: Gary Gershoff/Getty Images North America)