Where did the name "Guardians of the Galaxy" come from?

They did drop John C. Reilly's line "They're calling themselves the Guardians of the Galaxy" from the final release of the film. I also noticed that Drax is not in the lineup scene in the film, as he was introduced later. I think he was included in this part of the trailer so that all five main characters could be introduced in a similar way.

To answer your question, yes, Ronan the Accuser is the first to use the name "Guardians of the Galaxy" in the film. Peter Quill (Starlord) and Rocket do talk about saving the galaxy in earlier scenes, but they don't use the titular phrase until after Ronan coins it.

In the comics, there is some confusion as to where (more accurately, when) the team's name comes from as well. The "original" Guardians of the Galaxy come from 1000 years in the future, but those comics were published decades ago (in the late 1960s an early 1970s, then again in the early 1990s). That team traveled into the past (creating alternate timelines, as one does) and influenced the current team to take the name. So the current Guardians of the Galaxy took the name from a team that existed before them and 1000 years after them. Adding to the confusion, at least one character (Vance Astro, aka Major Victory) was a member of both teams, so it's not entirely clear whether or not the two teams influenced each other to take the same name, which would be a paradox.