As someone who loves Your Name so much, I'm glad you enjoyed it as well. Otherwise, I'm mentioning it in this comment to recommend it to you.
If you want a heavy and serious plot: Steins;Gate. It's tagged sci-fi and thriller, and is about time-travel. You might get sleepy at the first few episodes, which slowly build the setting, but it didn't get an almost perfect score of 9.13 on MyAnimeList for nothing, imo.
The Promised Neverland is also my personal must-watch. It has the three tags you're looking for. Without spoiling too much: the main characters are little orphan kids who try to escape their orphanage once they find out the truth about the adults and the orphanage itself. Season 2 is coming in October this year.
Death Parade is also a good one, imo. It's about a bar which is a 'temporary stop' for those who pass away. The arbiter judges them in the said bar in various ways to figure out if they were good or bad people in life (because apparently he doesn't know for certain lol) to determine whether they deserve heaven or hell.
For the movie, I think Weathering With You is the must-see lately. I haven't seen it myself, though. And it's not a horror/mystery/thriller, but is a drama.
Thanks for including the plot summary!