Of course you can. Entire comic book universes have been upended dozens of times, in crisis (or Crisis) after crisis and have managed to still exist with the same name. The details change. The story remains the same.
I loved The Sandman comics. I love The Sandman TV show and desperately hope for a second season. Changes were made in the show to reflect modern sensibilities. Some people had their gender and/or skin color changed. Some people, especially female characters, got stronger, more proactive roles. They didn't show on-screen rape like the comic had (and that rape was, in the comic, a character-defining moment for the rapist). Two characters got merged into one, and made into a much better (i.e., kinder and more story-logical) person in the process. Dream himself is somewhat kinder. The story was the same, and still just as good, but the details have made the story better for modern audiences--and quite frankly, better for me, a long-time fan, as well.
What is the story of Dragonlance? Keep that story, and improve the rest.