Well here's a list of casualties in Husayn's army at the battle.
As far as i can see there are a few man identified to be Persians or who have been settled down in Kufa etc. among them: Nasr ibn Naizar (May Allah be pleased with him) who's the only one listed as a Persian or (as a freed slave) coming from Persia in that list.
From Kufa as it seems -I'm just trying to analyze the list- you'll find much more:
Hani ibn Orwah, the two brothers Sa'd and Abdul Hatoof Ansari, Zuhayr ibn al-Qayn al-Bajali (one of the commanders on the site of Imam al-Husayn (may Allah be pleased with him)), Jahib ibn Hajjaj at-Taymi, Habib Ibn Amir e Taimi, Sayeed Ibn Abdullah Hanafi, the two cousins Saif Ibn Hars al Jabiri and Malik, Zarghamah Ibn Malik e Taghlabi, Aabis ibn Abi Shabeeb al-Shakiri, Abdullah Ibn Bushr Khashami, Abdul Rahman and Abdullah sons of Orawah Ibn Harraq al Ghaffari, Omer Ibn Zabiah Az Zabiyee and Nafi ibn Hilal al-Jamali.
But those names are just what i conclude from the list above so maybe i added or forgot some by mistake. Maybe some history books could give you more help as these people might not necessary be Persian while other's in the list could be so as Kufa was part of the Sassanid empire as @Shoaib stated but this don't necessary mean that all people from there who participated in that Battle were Persian!
According to Shi'a references one can add the following Names:
Aslam ibn 'Amr اَسلَم بن عَمرو (in the above list the freed slave Aslam?), Rafi' ibn Abdullah (in tha above list the freed slave Rafe?) رافع بن عبدالله, Zaher (Zahir) ibn 'Amr (al) Kindy زاهر بن عمرو کندی (in the above list Zavir ibn Amro al Kandi?), Fayruzan and Nassr ibn Abi Nouzayr (=Nasr ibn Naizar?) فیروزان و نصر بن أبی نیزر. [As quoted in the comment and link from @Shia_Sunni_________UNITY]
And Allah knows best!