Technical note / Defect ('illah): (2) In manuscript (Z) this word is written "Jinab" (with jim and nun) instead of "Khabbab" (with kha' and ba'), while in the rest of our manuscripts the dots on these two letters are not clear. However, in manuscript (S) it can possibly be read as "Khabbab".
General principle: This (Khabbab) is what is established in Khalifah bin Khayyat's "al-Tabaqat" (in both edited editions: al-'Umari's edition p. 11, and Suhayl Zakkar's edition p. 40). It also agrees with the printed edition of Ibn 'Asakir's "Tarikh Dimashq" (volume 19, edited by Ma'mun al-Saghirji), where all three manuscripts have "Khabbab". In all the other places where Ibn 'Asakir mentions the mother of Khalid bin Sa'id bin al-'As, he quoted her name from Khalifah bin Khayyat and others on pages (510 to 513).
Note / Clarification: However, on page 511, while quoting Khalifah's statement, Ibn 'Asakir said: "His mother is Lubaynah bint Khabbab, and in the original of our hearing it is 'Jinab'..." Then a little further on Ibn 'Asakir said: "And Khalifah mentioned it in another place, saying 'Lubaynah bint Khabbab'." It is as though Ibn 'Asakir wanted by this to affirm that "Khabbab" is indeed the correct name of her father. And Allah the Exalted knows best.