As long as the postcode is complete, there are only few full addresses that the postie needs to check against. If you got a letter the same day to your full address and your name is unique, then it would be fairly quick to find you.
BTW in Scotland at least, during the Christmas period, it is customary to leave a Christmas card for the postie outside with a small bank note in it. An easy way to say thank you for their efforts and to ensure that the postie will remember your name even better next time ;)
Customary (and extremely welcomed by the many postmen & women I've had the pleasure to know, my father having worked for Royal Mail / CWU) in England as well as Scotland (and I'm sure in Wales/NI too - probably elsewhere as well, and even in places where it's not customary it won't do any harm to thank people providing year round services to you with a small gift once a year!)
Also, while I agree with you that in this case (having a full postcode as well as name) it would have likely been an easy task for the local postie, Royal Mail do actually have a small team* of people who work in figuring out more tricky ones, so if a local person can't work it out for being on their beat it can be sent to the "address detectives" (great title!) to try to solve.
* My knowledge is both 20 years out of date and fuzzy in my memory, so I've no clue how big a team it is nor if there's enough confusingly-addressed items to need anyone working on it full time, or if it's just one aspect in a wider set of responsibilities that a team does when needed.
BTW in Scotland at least, during the Christmas period, it is customary to leave a Christmas card for the postie outside with a small bank note in it. An easy way to say thank you for their efforts and to ensure that the postie will remember your name even better next time ;)