The noun ibtisam is not in the Quran, but its root appears once: when Sulayman heard the ant warning its fellows, “he smiled (tabassama), amused at its words, and said: My Lord, inspire me to be grateful for Your favour” (27:19).
Meaning of the name Ibtisam
Ibtisam is the verbal noun of ibtasama, “to smile”, from the root b-s-m (basma, “a smile”): the smile, the light laugh that barely shows the teeth. The name is common in the Maghreb (Ibtissem in Tunisia and Algeria, Ibtissam in Morocco) and the Middle East.
So [Solomon] smiled, amused at her speech, and said, "My Lord, enable me to be grateful for Your favor which You have bestowed upon me and upon my parents and to do righteousness of which You approve. And admit me by Your mercy into [the ranks of] Your righteous servants."