Now, wait. Are you talking about the obvious, intentional use of the element "adwords" -- or about the random occurrence of the string "...adwords..." in the course of a name? Admittedly that's a pretty long string for randomness. But, for comparison purposes, I once had a confusing experience involving an ad blocker and some standard emoticons whose names, in code, were "mad", "glad" and "sad". (I did not figure it out myself.)
Suppose your domain name is some long Hungarian word* and you just looked at it with fresh eyes and realized it's got "adwords" in the middle. Now what do you do?
* This example is linguistically impossible. Just so you know I'm not talking about any actual site.