They probably figured they could use Wakina to refer to the thunderbird, and intended “Hawk Bow” to parallel “Thunderbird Rifle” as a less powerful weapon, as hawk is a bird lesser than the Wakíŋyaŋ.
Not to say these names are historically accurate (they aren’t), just that they did care about the aesthetics of names, the names weren’t chosen at random, and you can suss out the logic behind them.
Compare the Haud units, where the pattern of all three loanwords is names of weapons: Aenna (bow), Tomahawk (actually an Algonquian word), and Kanya (“stick”, by which the devs intended the war club). Their source is probably a word list like this:
68 Bow Aeana
69 War club Yeanteriyohta kanyoh(Taken directly from here, original source is Notes on the Iroquois, or, Contributions to the statistics, aboriginal history, antiquities and general ethnology of western New York)
Or this:
53 stick (of wood) kà:nhia/kaná:kareFrom wiktionary:
https://en.wiktionary.org/wiki/Appendix:Algonquian_and_Iroquoian_Swadesh_lists