Unfortunately that's the reality for a bunch of business. Google has an interest to encourage companies to pay for their own brand terms. I cant see it going away, for a decade+ google has been reducing people ability to manage campaigns and they lump more together so its a 'we'll manage that for you' enviroment.
That said make sure you are paying bottom dollar as best you can to win these KWs. Keep it separate from other generic business campaigns as much as possible. Make sure your using exact matches etc and not just broad/phase and see how low you can push down specific terms and rank.
Depending on the word itself , if it is unique you might want to take it to a regulator for discussion. Google must like to avoid this type of attention and while low odds you may get lucky. Adwords in general is seriously over due so greater attention in their updates.
Also there always a rebrand/cloned product option.
I wasn't sure what you mean by "This is causing us to pay a high price for traffic we've already paid for" is this in a return visitor thing searching your name and then going to competitors? I guess you have to make sure your taking advantage of a visitors time while you have them with details capture and social etc so you can engage organically.
