If I'm understanding your question, what you're asking is if, instead of having two accessories, you can have two hats?
If that is the question, then, no, you cannot have two hats at a time. You can only wear one hat, one pair of shoes, one coat, and two accessories.
However, you can still receive a second hat as a reward - but you will have to sell one. Just remember to compare the two and see if the new one is better than what you have.
As you get to the next level of favours, there will be different hats, accessories, etc. offered - so make sure you compare!