Roll for Initiative!
JavaScript (ES7),  73  60 bytes
-13 bytes by just sorting the input without isolating the names, as suggested by @asgallant
Expects a list of [SPD, DEX, WHT, Name].

a=&gt;a.sort((a,b)=&gt;(g=([s,d,w])=&gt;~(s*s/(d*d)**.25)+w)(a)-g(b))

Try it online!
How?
To save a few bytes:

we compute \$-\text{Initiative}-1\$ instead and sort the list the other way around
we compute \$\sqrt{|\text{DEX}|}\$ as \$(\text{DEX}^2)^{\frac{1}{4}}\$