Although it’s still very early, several candidates have already expressed their interest in the 2020 Libertarian Presidential nomination. The Amarillo Pioneer profiles declared candidates for the nomination Adam Kokesh, Ben Leder, Arvin Vohra, and Daniel Behrman. A discussion in the FB group LP 2020 Delegates – unofficial mentions that Vermin Supreme, Kim Ruff and Sandra T. Salas (a satanist stripper who ran as an LP candidate in 2018 in PA) are in the running as well.
Vohra, Leder, Behrman and Ruff participated in a debate on December 11. According to comments on that post “Other candidates that are missing are:…Zoltan Istvan, Cecil Ince, Donald Eugene Lowe, Derrick Micheal Reid and William Hurst”.
Bill Weld is widely believed to be running as well, but has made no formal announcement. Larry Sharpe, who was rumored to be a likely candidate previously, has said he is unlikely to run following a 1.6% showing for Governor of NY (although that was the best Libertarians had ever done for Governor in that state, earning them ballot retention in NY for the first time ever).
Some additional candidates are listed at http://www.politics1.com/p2020.htm but they include some who have already said they won’t run, such as Mary Ruwart.