Covering Head During Prayer
Do I have to wear something on my head (turban or hat) while offering prayer?
It is well-known that the Prophet (peace be upon him) was never seen without a head-covering. However, there is no an authentic hadith in the Sunnah that necessitates covering the head while offering prayer.
The general principle is to wear clothes that are respectful during prayer. If in the culture you are in it is respectful to wear a head-covering (or disrespectful not to!), then do so out of an intention to be respectful to Allah.
Regarding the ruling of covering the head while praying:
1- The majority of scholars are of the view that it is merely permissible to cover your head during prayer. There is nothing wrong with praying without a turban because the head is not `awrah, and it is not obligatory to cover it whilst praying, whether one is praying as an imam, praying alone or following an imam.
2- Imam Abu Hanifah had an opinion that it is disliked to offer prayer without covering head.
To get more information about the rulings of covering the head in prayer, you can watch this short video with Dr. Muhammad Salah.
Source: Huda Youtube Channel.