I'm basically asking exactly this question but for boolean operations.
"Operand" works well for "NOT" because there's only one operand, but I'm especially interested in operand names for "AND" and "OR" etc. operators to try to avoid calling things, "operand1" and "operand2."
If you want to distinguish between the two operands in statements such as
$$a \vee b$$
$$a \wedge b$$
the convention typically used is to call $a$ the "first operand" and $b$ the "second operand." If the operator is conjunction, then one could say $a$ is the "first conjunct" and $b$ is the "second conjunct." If the operator is disjunction, then one could say $a$ is the "first disjunct" and $b$ is the "second disjunct." All of these are equivalent in meaning. Note that due to commutativity $a$ or $b$ could easily be listed as the first or second operand, so the choice of which is arbitrary.