Ismail connects first to his own noble Arabic name, and also to the Qur’anic figure of Ismail عليه السلام. A secondary search for patience and sacrifice may also be meaningful.
يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ ٱصْبِرُوا۟ وَصَابِرُوا۟ وَرَابِطُوا۟ وَٱتَّقُوا۟ ٱللَّهَ لَعَلَّكُمْ تُفْلِحُونَ
O you who have believed, persevere and endure and remain stationed and fear Allah that you may be successful.
ٱلْـَٰٔنَ خَفَّفَ ٱللَّهُ عَنكُمْ وَعَلِمَ أَنَّ فِيكُمْ ضَعْفًۭا ۚ فَإِن يَكُن مِّنكُم مِّا۟ئَةٌۭ صَابِرَةٌۭ يَغْلِبُوا۟ مِا۟ئَتَيْنِ ۚ وَإِن يَكُن مِّنكُمْ أَلْفٌۭ يَغْلِبُوٓا۟ أَلْفَيْنِ بِإِذْنِ ٱللَّهِ ۗ وَٱللَّهُ مَعَ ٱلصَّٰبِرِينَ
Now, Allah has lightened [the hardship] for you, and He knows that among you is weakness. So if there are from you one hundred [who are] steadfast, they will overcome two hundred. And if there are among you a thousand, they will overcome two thousand by permission of Allah. And Allah is with the steadfast.
قَالَ سَتَجِدُنِىٓ إِن شَآءَ ٱللَّهُ صَابِرًۭا وَلَآ أَعْصِى لَكَ أَمْرًۭا
[Moses] said, "You will find me, if Allah wills, patient, and I will not disobey you in [any] order."
وَخُذْ بِيَدِكَ ضِغْثًۭا فَٱضْرِب بِّهِۦ وَلَا تَحْنَثْ ۗ إِنَّا وَجَدْنَٰهُ صَابِرًۭا ۚ نِّعْمَ ٱلْعَبْدُ ۖ إِنَّهُۥٓ أَوَّابٌۭ
[We said], "And take in your hand a bunch [of grass] and strike with it and do not break your oath." Indeed, We found him patient, an excellent servant. Indeed, he was one repeatedly turning back [to Allah].