Your post piqued my interest as a history buff and got me doing some checking.
Regarding Arab presence in Japan during the days of the Ottoman Empire, the only thing that I could think of was the shipwreck of the Ottoman frigate Ertuğrul in 1890, off the coast of Wakayama Prefecture. This is a famous incident in the relations between Japan and Turkey in establishing longlasting ties of goodwill between the two nations. According to what I've learned from the media, Turkish children are taught about the incident, and many Turkish feel a strong bond of friendship with the Japanese. This is the Wiki article on the incident:
Ottoman frigate Ertuğrul - Wikipedia
This probably is the cause of the claim of Arab presence in Japan, but the article says that all survivors from the ship were repatriated to Turkey. So, I wonder if there had been Arabs who remained in Japan.
Regarding your family name, "Itani" is not an uncommon name in Japan as thomas said. However, the name "Itani" can be written in many kanji variations, of which 井谷 and 伊谷 are the most common. So, it is quite difficult to say which Itani families have Arab ancestors. There is a surprising coincidence, however. The largest concentration of 井谷 (the former) households can be found in Wakayama Prefecture.
This is as far as I know and can research on the Web. If you wish to explore further, I suggest you contact the Japan Arab Association here in Tokyo. They may have more information and contacts who are more knowledgeable.
Address:
Japan Arab Association
c/o Cosmo Oil Co., Ltd.
1-1-1 Shibaura, Minato-ku
Tokyo 105-8528, Japan
Phone: +81-3-3798-3515
Good luck!
Edit: I have written the snail mail address because the Association does not accept email inquiries and does not disclose its email add. I think you can write in Arabic or English to them.