In a 'kokushibo meets tanjiro fanfiction', one possibility is that Kokushibo senses something different about Tanjiro right away. Maybe it's the fact that Tanjiro has a unique scent or an energy that Kokushibo has never encountered before. Tanjiro, being Tanjiro, would be ready to face Kokushibo head - on, but also be open to communication if there's a chance. The story could explore their different views on the world of demons and slayers, and how they might come to understand each other better through their encounter.
For Tanjiro, he could become more understanding of the complex nature of demons. Meeting Kokushibo, a powerful and complex demon, might make him realize that not all demons are simply evil. Kokushibo, on the other hand, could start to have some doubts about his loyalty to Muzan. Tanjiro's tenacity and belief in the good of all might start to chip away at Kokushibo's cold - hearted exterior.
How about 'Giyuu x Shinobu: The Jealousy Factor'? This title clearly shows the relationship between the two characters and the key aspect of jealousy. It gives a hint to the readers about what the fanfic might be about, which is the jealousy that could exist in their relationship.
One great 'shinobu and giyuu fanfic' is 'The Unspoken Bond' which delves deep into their complex relationship. It shows how they gradually come to understand and support each other in the face of various challenges in the Demon Slayer world.
The battle of Yoriichi vs Kokushibo can be found in the advanced stages of the Demon Slayer manga. It's an intense and highly anticipated confrontation. The build-up and action are both masterfully depicted.