If you are among the first persons to take a Y-DNA test for your surname or your specific line of a surname, often you will not have any matches.  This may be disappointing, though it is only a matter of time until you have a match.  When you don't have any matches, the best approach is to find some other males with your surname to test.  To validate your lineage, it is recommended that you test the most distant cousin in your family tree.  His result should match, or be an extremely close match, to your result.  This step of testing another male in your family tree will scientifically validate your result.  On the other hand, you may have a lot of matches with other surnames, especially if you are Haplogroup R1b, and you are testing only 12 Markers.  It is very tempting to pursue these matches with other surnames, in the hope of finding a lost relative from the family tree.  Matches with other surnames are most likely not relevant in a genealogical time frame.

If we consider for a moment: how many males had your Y-chromosome result, or a close result, in the 1300's, when surnames were being adopted.  This figure could be in the hundreds, if not in the thousands.  Each of these males, or small groups of males in a family unit at the time, probably adopted a different surname.  These males were probably also spread out geographically.

If we take this group of males who adopted hundreds of surnames in the 1300's, and then consider that each surname probably took on multiple forms through the centuries until the 1900's, plus factor in the number of possible male descendents today - we have a very large number of surnames that could share a Y-DNA result.  Most people in England adopted surnames by 1400, which is a little over 600 years ago.  In a time frame of 600 years, depending on the figure used for years per generation, we would expect between 20 to 24 generations to have occurred, at 30 years per generation or at 25 years per generation.  The current mutation rate estimated for the Y-DNA Markers by the scientists is 1 mutation every 500 generations per Marker.  For a 25 Marker test, we would expect 1 or maybe 2 mutations if two people were related in the 1400's, in the time since surnames were adopted.  Most likely a match with another surname is the result of being related before a genealogical time frame, or as a result of convergence.  See the DNA-101 article on CONVERGENCE

Convergence is where Y-DNA results mutate over time, and as a result of changes, these two results now overlap.  Depending on your ancestral country, and the surviving records, your family tree may be traced back to the 1800's, 1700's, or 1600's, and for a few rare family trees, to a time well before then.  If a 25/25 match with another surname is a result of a family taking in an orphan in 1425 - you will probably never find the paper record, if a paper record ever existed, and pursuing the match takes valuable time away from traditional family history research.  As more people take a Y-DNA test, you will eventually have matches with other surnames.  For a-12 Marker test, the total range of generations for relatedness is 76.9, which is almost 2000 years, and well before the adoption of surnames.  

Those who belong to Haplogroup R1b will have many matches with other surnames.  In fact the dramatic population expansion within Haplogroup R1b lead the FTDNA science team to clearly see the need to expand the original testing panel from 12 to 25-markers and later to 37-markers.  Pursuing matches with other surnames is normally not necessary, unless there is some genealogical evidence to support such a match.  For those interested in pursing the match, an upgrade to 37-Markers is recommended.  Even at 37-Markers, you may have matches with other surnames, especially for Haplogroup R1b, and as a result of convergence. In rare cases, the match could indicate an unknown variant of the surname.

DNA testing is a tool to be used with your family history research.  DNA testing provides additional information which is evaluated in conjunction with your family history research.  If you have researched your family tree to the mid 1800's, pursuing a match with another surname that might have occurred from 1400 to 1800 is probably not the best investment of time.

Matches with other surnames can have value for those who are not R1b, and whose ancestors have migrated and they are trying to identify the county of origin in the ancestral homeland.  People frequently moved in the past, though often the distances were not very far per generation.  Therefore, a cluster of your Y-chromosome and close matches would exist in the ancestral county.  For those whom you match with another surname, these matches can often be used to identify the ancestral county.  If you are able to find enough matches who know their ancestral county, and one county is reported by a high percentage of matches or close matches with other surnames, you would have a clue as to the ancestral county.  It is very tempting to pursue matches with other surnames, in the hope of finding a lost relative from the family tree.  Matches with other surnames are most likely not relevant in a genealogical time frame.