A Haplotype is established by the 12-Marker result from testing the Y-Chromosome.  Some Haplotypes are common, with a high frequency of occurrence and some Haplotypes are rare, with a low frequency of occurrence.

Many people have common Haplotypes, which means that they would expect to find matches to those who do not have their surname.  This occurs because we were all at one point related.  As the different branches of the Adam + Eve tree evolved throughout time, mutations occurred, forming different Haplotypes.  Thousands of years later, there are have many different Haplotypes. 

Due to these mutations, you could have two unrelated branches of the human family tree that mutate to an identical Haplotype.  This is called convergence.  If your Haplotype matches an individual with a different surname, and your genealogy research shows no evidence of an extra-marital event or an adoption, your match may be the result of Convergence.

The example below shows convergence between the ABC surname and the XYZ surname, using just 3 markers to keep the example simple.  Notice how the mutations over time bring two different Family Lines to the point that they match.  Convergence explains why a haplotype will match others with a different surname.

DNA testing for genealogy is not a substitute for genealogy research, but is instead a companion.  Results that match must be considered in light of the genealogy research.   If you match someone with a different surname, most likely there wasn't an adoption or extra marital event, and your match may be the result of convergence.