Trying to return more than just the top result from sklearn NearestNeighbors
My guess would be that in the following piece of code:

for i,j in enumerate(indices):
  temp = [round(distances[i][0],2), clean_org_names.values[j][0][0],unique_org[i]]
  matches.append(temp)


The variable (array element):

distances[i][0]


contains the top element match for the $i^{th}$ line. Replace the second array index so it becomes:

distances[i][1]


You may want to increase one of the two zero indices in the following line as well to have a distance like value:

clean_org_names.values[j][0][0]