It depends on the surname. At least in Europe, many of them are descriptive and can belong to a great many totally unrelated people. I will make examples in English but I know many like this in my languages, Italian and Greek.
ACKER = Denoted a person who lived near a field, derived from Middle English aker or Middle High German acker meaning "field".
MASTERSON = Means "son of the master" from Middle English maister.
MILLHOUSE = Name for someone whose house was in a mill or who worked in a mill.
NEWMAN = Means "new man, newcomer" from Old English neowe, niwe, nige and mann.
TOWNSEND = Means "dweller at the town's end".
ACKERMAN= Means "ploughman", derived from Middle English aker "field" and man.
BAKER = Occupational name meaning "baker",
BARBER = Indicated a barber, one who cut hair for a living.
BOND = Occupational name for a peasant farmer
MAYER = Occupational name for a mayor, from Middle English mair.
PORCHER = Means "swineherd" from the Old French and Middle English word porchier.
PORTER = Occupational surname meaning "doorkeeper", ultimately from Old French porte "door", from Latin porta.
POTTER = Occupational name for a potter, one who makes earthen vessels.
SMITH = Means "metal worker, blacksmith" from Old English smiþ, related to smitan "to smite, to hit". It is the most common surname in most of the English-speaking world.
ADAMSON = son of ADAM
ANDERSON, ANDREWS =son of ANDREW".
CHRISTIANSON =son of CHRISTIAN".
CHRISTOPHERSON =son of CHRISTOPHER".
DAVIDS, DAVIDSON =son of DAVID".
ERICKSON, ERICSON =son of ERIC".
Place of origin
AINSWORTH English (Habitational name for a person from the village of Ainsworth near Manchester,)
MARLEY = Originally denoted a person who hailed from one of the various places in Britain called Marley, ultimately meaning either "pleasant wood", "boundary wood" or "marten wood" in Old English.
NEWTON = From the name of one of many English towns meaning "new town".
LONG = Originally a nickname for a person who had long limbs or who was tall.
MARTEL= Nickname for a smith, derived from old French martel "hammer",
SHARP = Nickname for a keen person, from Old English scearp "sharp".
SHORT= From a nickname for a short person, from Middle English schort.
STARK = From a nickname meaning "strong, brave" in Old German and Old English.
WHITE = Originally a nickname for a person who had white hair or a pale complexion, from Old English hwit "white".
YOUNG = Derived from Old English geong meaning "young". This was a descriptive name to distinguish father from son.
FUN FACTS ABOUT ITALIAN SURNAMES:
The most common of all:
In Italy, one of the most common surnames is Rossi, which means Red (and was probably given to redheads rather than communists, who didn't exist at the time). Here is a map:
Here are the most common in decreasing order. As you see, they are all but one descriptive rather than occupational or denoting place of origin.
1 Rossi 45.677 (= red)
2 Russo 31.372 (= red)
3 Ferrari 26.204 (= smith, the one who works with iron, "ferro")
4 Esposito 23.230 (= comes from "esposto", exposed, a baby left by its parents)
5 Bianchi 18.794 (= White. Denoting either skin or hair)
6 Romano 17.947 (= Roman)
7 Colombo 17.670 (= dove. It's the surname they very often gave to babies left by their parents)
8 Ricci 15.045 (= Curly)
9 Marino 13.417 (= marine, of the sea)
10 Greco 13.416 (= Greek)
11 Bruno 13.108 (= Brown haired)
12 Gallo 12.902 (= French)