You cannot, without licensing the character.
The only license under which you can freely distribute 5e content is the OGL:
Permission to copy, modify and distribute the files collectively known as the System Reference Document 5.0 (“SRD5”) is granted solely through the use of the Open Gaming License, Version 1.0a.
You cannot use any "Product Identity" under the OGL without specific licensing:
- Use of Product Identity: You agree not to Use any Product Identity, including as an indication as to compatibility, except as expressly licensed in another, independent Agreement with the owner of each element of that Product Identity.
...And "Product Identity" encompasses character names (emphasis added):
"Product Identity" means product and product line names, logos and identifying marks including trade dress; artifacts; creatures characters; stories, storylines, plots, thematic elements, dialogue, incidents, language, artwork, symbols, designs, depictions, likenesses, formats, poses, concepts, themes and graphic, photographic and other visual or audio representations; names and descriptions of characters, spells, enchantments, personalities, teams, personas, likenesses and special abilities; places, locations, environments, creatures, equipment, magical or supernatural abilities or effects, logos, symbols, or graphic designs...
The following items are designated Product Identity, as defined in Section 1(e) of the Open Game License Version 1.0a, and are subject to the conditions set forth in Section 7 of the OGL, and are not Open Content: Dungeons & Dragons, D&D, Player’s Handbook, Dungeon Master, Monster Manual, d20 System, Wizards of the Coast, d20 (when used as a trademark), Forgotten Realms, Faerûn, proper names (including those used in the names of spells or items), places,
If you're just pulling names from the suggested names in the races section, the infringement might be minor enough that nobody will care. You might even be able to claim that it was a coincidence, since many of those are just generic fantasy jumbles anyway. However, there's no explicit exception for those names, so you're still technically violating the OGL.