This message was posted by a user wishing to remain anonymous
I am not a lawyer; the following is my understanding and/or opinion. For a final say, I encourage you to discuss this with your legal counsel.
If you want to fight it, that's your choice - as a Compliance analyst, I enjoy accuracy and organization. However, do you need to? Probably not. I feel the only reason one might push to correct this is to avoid potential complications or some other failure in the relationship (non-payment, for example) which may prompt legal action to remedy. Effectively, the whole relationship is a contract or quasi-contract (regardless of whether names were spelled correctly), and in the end, the claimant of the relationship would likely have a valid claim for unjust enrichment against the offender. Your legal counsel, however, would have a better understanding of the jurisdiction involved to confirm this.
So, to me, it seems like something where you're trying to decide when you want the headache. At the start of the relationship, or in the potential that the relationship sours (mind you, the sour point may also include legal fees). However, I'm not sure anyone here can give you an answer with 100% certainty without knowing the jurisdictions involved, what your business does, etc. So, I suggest you evaluate the need based on feedback from your legal counsel, the expected duration of the relationship, and how much of a risk this TP/vendor is categorized as.