What's a better word for "cowardly", that doesn't sound like name-calling?

Sounds like a case for understatement for ironic effect, such as "less than forthright"

I don't think using pusillanimous would be understood by most readers, and using the word can make you seem pretentious (which may or may not be your intention).

To describe the actions taken by this other person, you might say that they are hiding behind anonymity in order to make these attacks. It is not a single word, but it tends not to be completely accusatory while still describing their actions.

A number of alternatives are suggested here, including faint-hearted, scared, spineless, base, weak, shrinking, fearful, craven, dastardly, timorous and pusillanimous (as already suggested).

It can't really be said that any of these avoids a hint of name-calling, and, depending on the nature of the attack, perhaps shrinking, weak, scared, and timorous could be ruled out. I personally would be inclined to go with craven, although that might sound a little archaic.