Got you covered — I spent some time pulling together a clan-sorted roster for 'Naruto' that focuses on the major shinobi families and their most recognizable members. Below I group clans and list notable characters under each one so you can scan by family quickly.
Uzumaki: Naruto Uzumaki, Kushina Uzumaki, Mito Uzumaki, Nagato (Pain) Uzumaki lineage, Karin Uzumaki, Boruto Uzumaki, Himawari Uzumaki.
Uchiha: Sasuke Uchiha,
itachi uchiha, Fugaku Uchiha,
mikoto uchiha, Shisui Uchiha,
madara uchiha, Obito Uchiha, Izuna Uchiha, Sarada Uchiha.
Hyūga: Hinata Hyūga, Hiashi Hyūga, Neji Hyūga, Hanabi Hyūga, Hizashi Hyūga.
Senju & related: Hashirama Senju, Tobirama Senju, Tsunade (Senju descendant), Nawaki (related), and classical Senju descendants.
Nara: Shikamaru Nara, Shikaku Nara, Shikadai Nara.
Akimichi: Chōji Akimichi, Chōza Akimichi, Chōchō Akimichi.
Yamanaka: Ino Yamanaka, Inoichi Yamanaka, Inojin Yamanaka.
Inuzuka: Kiba Inuzuka (+ Akamaru), Kurenai’s students and extended Inuzuka relatives.
Aburame: Shino Aburame.
Sarutobi: Hiruzen Sarutobi, Asuma Sarutobi, Konohamaru Sarutobi.
Hatake: Kakashi Hatake, Sakumo Hatake.
Hōzuki & Hoshigaki (Kirigakure/other): Suigetsu Hōzuki, Kisame Hoshigaki.
Ōtsutsuki (extra-terrestrial bloodline):
kaguya ōtsutsuki, Hagoromo Ōtsutsuki,
hamura ōtsutsuki, Momoshiki Ōtsutsuki, Kinshiki, Urashiki, Toneri Ōtsutsuki, Isshiki Ōtsutsuki.
Other surnames worth noting: Namikaze (Minato Namikaze), Shimura (Danzo Shimura), Umino (Iruka Umino), and village-specific families like the Sunagakure Sand siblings (Temari is allied by marriage into the Nara line via her child).
This list focuses on the best-known clan groupings and named members who matter in the main story and sequel. If you want this expanded into an exhaustive table that includes every filler, side character, academy student and lesser-known branch, I can keep building it, but for now this is a tidy clan-sorted snapshot — I love seeing how family ties shape so many plot threads in 'Naruto', it always makes rewatching more satisfying.