Renal damage is not mentioned as a side effect of Suboxone, but there are some case reports in the literature of kidney failure associated with buprenorphine use. Recall that buprenorphine is one of the two active ingredients in Suboxone.
In both of the only two cases on the PubMed search engine, kidney failure happened in the context of liver failure.
One case tested positive for Hepatitis C, while the other case happened in a person who was misusing Suboxone by snorting it. If you use Suboxone as prescribed and are otherwise healthy, it is highly unlikely you will have kidney failure from medications containing buprenorphine, like Suboxone.
The other active ingredient in Suboxone, naloxone, is also safe from the standpoint of renal function. There are no known adverse effects of naloxone on kidney function. In fact, some studies indicate it might reverse the toxic effects on the kidney of other opioids, like morphine.
Naloxone has an opioid blocking component that prevents people from abusing Suboxone by injecting or snorting it and stops any experience of euphoria.
Studies show that for people whose kidneys are not functioning optimally, for example, people with renal insufficiency or who require hemodialysis, buprenorphine is a completely safe medication.
Buprenorphine is primarily metabolized by the liver, so there is no need to even adjust the dose in people with chronic kidney disease. This is in contrast to many of the other opioids which do require the kidney to metabolize them and their by-products. Buprenorphine is therefore recommended as a first-line choice for the treatment of pain in people with chronic kidney disease.