Presidential primary candidates get on presidential primary ballots in New Mexico automatically if the parties believe they are bona fide candidates. Democratic candidates who will be on automatically this year are Hillary Clinton and Bernie Sanders. Republicans are Jeb Bush, Ben Carson, Chris Christie, Ted Cruz, Carly Fiorina, John Kasich, Marco Rubio, and Donald Trump. Fiorina was put on the list just before she withdrew, so she remains on the ballot. See this story. The primary is June 7.
Other candidates can get on the ballot with a very difficult petition drive. This year the law requires 15,676 signatures (2% of the last presidential vote in the state). Any registered voter may sign. It is possible that Rocky De La Fuente is attempting this petition. No other presidential candidate has ever qualified for the New Mexico presidential primary ballot by petition. There is a U.S. House district distribution requirement; approximately 5,200 signatures must be gathered from each of the three districts.