Just a small notice from non-specialist, with a little access to literatures on Ainu in Japanese:

• Overwhelming majority of Ainu did not originally have family name. After Meiji Restoration, as stated in the following ordinances in early years of Meiji, they were forced to adapt the family (given)- personal name practice that also became standard among the Japanese after Meiji Restoration: 'Ex-Native People （旧土人: NB: with very strong pejorative tone!) those who have already had family name will keep it, but should only that in the current Japanese (July 19, 1876: from Nemuro office, Hokkaido Prefecture); 'The family name of 'Ex-Native People' should be standarized as those in 'usual' Japanese (August 1876: also from Nemuro office, Hokkaido Prefecture)'. (Emori 2007: 390; Sekiguchi et al. 2015: 147)
• Even before then, however, Ainu people had seemingly had some kind of kinship consciousness: The males those who belonged to the same patrilineal group were called by this group name, ekasi ikiri, and they shared the same ancestoral symbol, i-tokpa. On the other hand, the female those who belonged to the same matrilineral group were called by this group name, huchi ikiri, and they shared some tied rope amulet called ra-un-kut or menoko-upsor. These kinship concept did not correspond well with the concept of Japanese 'family', though (Emori 2007: 390f.).

 

I strongly recommend to submit to this question also in /r/AskAnthropology/

Appendix:
Have you also ever referred to the following English site of old (now closed for new) Ainu Museum, Shiraoi? While being very concise, it's a kind of one of very few 'official' guide site on Ainu culture in English.

http://www.ainu-museum.or.jp/en/study/eng01.html

Some of the pages (esp. eng11.html) also mention their interesting custom of naming (not immediately give a name to new-born babies, instead just call them provisory, general (?) names).

 

References:

• Reports of Hokkaido Development Commissioners, with a Collection of Ordinances, Part I. Tokyo: Ministry of Finance, 1885, p. 487. (in Japanese)

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• EMORI, Susumu. Ainu Minzoku no Rekishi (A History of Ainu People). Chiba: So-fu Kan, 2007. (in Japanese)
• SEKIGUCHI, Akira et al. (eds.). Ainu Minzoku no Rekishi (A History of Ainu People). Tokyo: Yamakawa Pub.. 2015. (in Japanese)
• 'Can I get information which legislation and its issued year obliged Ainu People to be called in Japanese name during Meiji Period? (in Japanese)' Hokkaido Prefectural Library, Collective Database Reference, Feb. 10, 2017.

[Edited]: re-writes incomplete sentence (really sorry).