In the Qur'an, the name is simply "Zaid", with no additional names.

We know from sources like Tabari that his full name was Zaid al-Habib ibn Harithah ibn Sharahil ibn Abduluzza ibn Imri al-Qays ibn Amir ibn Al-Numan ibn Amir ibn Abdwalid ibn Awf ibn Kinana ibn Awf ibn Uzra ibn Zaidallat ibn Rufayda ibn Thawt ibn Kalb ibn Wabara ibn Taghlib ibn Talwan ibn Irmram ibn Al-Haf ibn Quda'a ibn Malik ibn Amr ibn Murrah ibn Malik ibn Himayr ibn Saba ibn Yashjub ibn Yarab ibn Qaltan.

Al-Habib ("the beloved") was a byname; Uzra was his clan; Kalb was his tribe proper; Taghlib was his super-tribe; Himayr was the general group of tribes in the area.

So are you surprised that the Qur'an simply calls him "Zaid"?

The names of the twelve Imams as believed in Twelver Shi'a Islam are:

1. Ali ibn Abu Talib
2. Hasan ibn Ali
3. Husayn ibn Ali
4. Ali ibn Husayn
5. Muhammad ibn Ali
6. Ja'far ibn Muhammad
7. Musa ibn Ja'far
8. Ali ibn Musa
9. Muhammad ibn Ali
10. Ali ibn Muhammad
11. Hasan ibn Ali
12. Muhammad ibn al-Hasan (al-Mahdi)