All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There is nothing wrong with supplicating for a specific person to be saved from harm that occurred or is expected. The Prophet supplicated for specific people among his Companions by their names in prayer.Abu Hurayrah narrated: “The Prophet used to recite the following invocations during Qunut: “O Allah! Save Salama ibn Hisham. O Allah! Save Al-Walid ibn Al-Walid. O Allah! Save ‘Ayash ibn Abu Rabee'ah. O Allah! Save the weak Muslims. O Allah! Be very hard on Mudhar tribe. O Allah! Afflict them with years (of famine) similar to the (famine) years of the time of Prophet Yousef.”
There is no specific form for supplicating for a specific person; rather a person supplicates according to the situation; if he is weak or oppressed, he supplicates for him to be saved, as in the previous Hadith. If a person feared for him, he supplicates for him to be preserved and protected, and if he was imprisoned unjustly, he supplicates for him that Allah would emancipate him from imprisonment, and so on.
Allah knows best.