Some candidate for the new swords:
1st: Kokindenjuu Yukihira or Kokindenjuu no Tachi, Hosokawa Yuusai's sword
2nd: Jizou Yukihira, a sword gifted to Akechi Mitsuhide from Hosokawa Tadaoki

Other guesses: Ookanemitsu, Tsuruga Masamune

The trailer showed us one of the swords reading an excerpt from Kokin Wakashu, an anthology of waka poem. The sword related to Kokin Wakashu is the sword Kokindenjuu Yukihira, Hosokawa Yuusai's favorite sword. More on his name origin can be read here. https://markussesko.com/2013/02/28/why-hosokawa-yusai-did-not-want-to-give-up-tanabe-castle/

Fun fact: The real name of Kokindenjuu's smith, Yukihira, is Kishin Dayuu. The first name can be interpreted as 'Demon God', hence his work is considered 'demonic'. Yuusai... what's with you collecting horror-related swords...

From the teaser, the swords seems to share scale-like tattoos. A zoom into the shoulder of the second sword seemed to have something like kikyou (?), Akechi Mitsuhide's symbol. Assuming this indicates the swords share the same smith, the sword might be- https://twitter.com/history_Mio/status/1254700068990382081?s=20

Jizou Yukihira, the sword that was given by Hosokawa Tadaoki to Akechi Mitsuhide.
Akechi Mitsuhide is in fact Tadaoki's father in law. Hosokawa Gracia mentioned in the trailer is Tadaoki's wife and Akechi Mitsuhide's daughter.
Despite their alliance, Tadaoki refused to shelter-

Mitsuhide when he was chased for killing Nobunaga in Honnouji. Perhaps, this is what the second sword means when "I betrayed that man".

Apparently the second sword wears an earring reminiscent to a shakujo, the staff that the monks (Jizou) carry. This adds into the argument that the second boy might be Jizou Yukihira.

Credits to @crimson_swallow for noticing!

I will add more stuff later. But if you are keen to check more and understand JP, you may want to check this thread for more info about these two! https://twitter.com/sohshu_notare/status/1254698654994034694?s=20