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Well in Ultima and like games theres always a split between using passive
and active noun in naming them-(Queen, King, Shield, Magician vs Swapper,
Advancer Withdrawer, Immobiliser etc). I mixed both to avoid being
repetitive, and to ease the search for finding the most appopriate word for
a piece, without being contrived.

Attaching -er suffix might help brand them as Ultima pieces and avoid
"encroaching" on existing Chess miscellany, but in any event the logic
behind names such "Ambassador", and "Cloak", should be pretty clear if
you read the piece descriptions...

Not so much the hunter/huntress pieces. Perhaps "proximator", and
"aproximator", would be more accurate. "Bully" could be a
"numerator", perhaps.