My taste, never overload your notation unless its necessary.
Many people in quantum information try to avoid "hats" or further ornaments for operators that are just linear maps. Simple capital letters are fine to write Hamiltonians, channels, unitaries and measurements (italics are not really important, but its a de-facto standard). When people write many-body hamiltonians in terms of smaller k-body interactions, it is common that they use low-case letters for the latter (example, the Hubbard model). Also, mind that in finite dimensional systems linear maps are in one-to-one correspondence to matrices.
On the other hand, thinking of linear maps as matrices forces you to choose a basis. It might be more clear in some contexts to use a symbol-with-hat to denote an operator without mentioning the basis and the same symbol without hat for a matrix representation. However, I find that this practice can make your notation more complicated without earning much, since typically there is a natural default basis in every problem.
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