Joseph,
I honestly don’t understand what you just said, but I’ll spell it out for you anyway:
You are not allowed to say Hashem’s name with your head uncovered. The M”B in 91:10 says that your shirt sleeve is an acceptable covering for this purpose.
The M”B in 91:12 says that for davening, one must wear a hat like he would wear when walking in the street or meeting with an important person, and that the small hat that is commonly worn under one’s hat is not sufficient (some have interpreted this to mean that two coverings are required, but as I stated before, I don’t hear it).
Just look in the Mishnah Berurah. This is all very clear.