The Ancestry Y-DNA database is pretty small. You may find some matches by entering your results at Y-Search. However, the best thing to do is to transfer your results to FTDNA and upgrade to 37-markers.

Initially, I would not put much effort into matches with other surnames, until you are pretty certain that a non-paternal event (NPE) has occurred. To obtain a genealogical connection, you need to match the time and place. About all you need to do initially is search the web with the two surnames to see if anyone has uncovered evidence for an NPE.

I would start by testing descendants of other sons of your documented family progenitor to determine the ancestral haplotype. This will eliminate recent mutations and give you a "cleaner" haplotype to compare to other families. Hopefully, they will have done the work to get their ancestral.

The current Y-DNA tests have limited utility and are a bit obsolete. The full Y-genome tests should prove to be much more useful as the prices decline. You may also want to take the autosomal tests at Ancestry.com, FTDNA (Family Finder) and 23andMe. They may match you with close relatives who have some useful genealogical information.