According to Amazon it's a light novel, same release date, publisher and total number of pages (192).
I personally own the first volume of the Kimi no Na wa manga physically, and the story is split into 3 Volumes, so if it's a manga they would've specified the volume.
I'm reading Vine reviews on Amazon and most of the reviews speak quite poorly of it as a light novel. Personally, I won't be purchasing this although I loved the movie.
I'm not aware of any other light novels besides this one that I ordered off Amazon, and the Another Side: Earthbound novel. I ordered the first one and figured I can order the other one at a later date.
The Kimi no Na Wa movie has both a light novel and a manga. Both expand some scenes and in the LN you can access the actual thoughts of the characters; it is written in first person narration). But IMHO the LN is almost a screen play of the movie, so do not expect to find too many surprises. The manga of KNNW is better in the sense that shows some "new" scenes and images to think about, I'd say 5% new material.
Additionally I strongly suggest you to read cannon light novel "Your Name. Another Side: Earthbound". It narrates parallel stories before and during the movie. There is also a manga of the same work, but I'd say the LN is far better, try reading it.
And in the same venue (filling gaps in the movie story), check u/BledaTG fancomic "Thoughts and Dreams" (beware, contains NSFW scenes, mainly some nudity from Taki not being Taki...), that extends on the "what happened" during their body swaps.
And for what happen _after_ the end of the movie, Makoto Shinkai supposedly* revealed that Taki and Mitsuha will get married in 2024 (by describing a picture of their wedding in Taki's Granma's house, in the "Weathering with You" light novel). Besides of that "fact", nothing is officially known about them. Zip, Nada.
There is plenty of fanfiction to explore about the "what next" after the end of the movie. I wrote a fanfiction about it, if you want to try: "Rediscovering the future" (in Ao3; it is also available in FFN). It resumes the story from exactly the final scene of KNNW.
Other fanfic I've read and I recommend are:
• "Kimi no Na wa: Future" by Alyena2x.
• "Remembering You" by Shining Arrows.
• "Reception" by Brishna.
[*] Supposedly because I've not read it but I've head that comment several times.
I don't know of a manga, but the novel is available online. https://www.amazon.com/name-light-novel-Makoto-Shinkai/dp/0316471860
Amazon link (not this summer, but next month actually)