Oda almost directly confirms a connection in Volume 96's SBS:
D: Odacchi!! A question!! Several characters have appeared with the name Shimotsuki, including Shimotsuki Yasuie, Shimotsuki Ryuma, Shimotsuki Kozaburo and Shimotsuki Ushimaru, but is there a connection with the place Zoro grew up in that bears that exact name, Shimotsuki Village, and Zoro's teacher Koushirou? So given how Zoro said he was taught the term "Sunacchi" by a geezer in his village and how in Volume 92's SBS you revealed how some came to the East Blue, it's starting to make sense! P.N. Yu-kun
O: Ah, yes. You might have to follow very closely to picture this, but...let me explain! It all starts with Shimotsuki Kozaburo (swordsmith and swordsman)
- He forges the "Enma" and bestows it to the heir of the Kozuki Family, Oden.
- 55 years ago, he sets out to sea!
- He and the samurai of Wano have a grand adventure!!
- They make landfall in a certain place in the East Blue.
- They save the locals from mountain bandits.
- They teach the villagers the way of the sword, who become enamored with swordplay.
- They decide to settle there, founding Shimotsuki Village.
- His son, Koushirou, is born.
- His granddaughter, Kuina, is born.
To put it in other words, who Zoro meant by "a geezer in his village" that he met was actually grandpa Shimotsuki Kozaburo-san himself, who comes from the Wano Country. Oh?
Then could that mean...Zoro's lineage...?! Well, the story of Shimotsuki Kozaburo, the samurai who founded Shimotsuki Village, is all I'm willing to share today!