In what era were family or surnames first deemed necessary and who decided on a family name?
The introduction of family names depended to some extent on social factors. The 'high and mighty' took on family names much earlier than the rest of the population. People who didn't move around much were also less likely to need family names than those who travelled a lot. In England and Wales there was legislation in the reign of Henry VIII (reigned 1509-1547) requiring all parishes to maintain and preserve registers of baptisms (and dates of birth), marriages and deaths. It seems that it was at this time that ordinary people adopted surnames. In England and Wales the family chose its own name. This was often an occupation (such as Baker, Cooper, Carpenter, Smith) or based on the father's name (Johnson, Williamson, Harrison, Thom(p)son, etc.) or based on placenames. Provided nobody was trying to deceive or pretend to be an aristocrat there was no objection to families choosing their own names. NOTE. Family names that end in -s (instead of -son) are generally Welsh (or of Welsh origin) - for example, Jones (instead of Johnson), Thomas (instead of Thompson), Harris (instead of Harrison).
Prince Williams' family name is Mountbatten-Windsor however the Royal Family don't tend to use surnames unless the situation requires it, in which case, the surname will be allocated depending on the person's title and status. Depending on the situation, the surnames 'Wales' or 'Cambridge' could also be (and have been) used by the Prince
Surnames were often bestowed upon persons displaying certain characteristics such as red hair (Reed family) or tall stature (Long family). They may have gotten their surname because they lived near a certain geographical feature such as a prominent rock (Hill, or Stone family) or a body of water (Lake, Pond, and Rivers families). Sometimes, people were even given surnames that derived from nicknames that stuck (Sharp, Quick, and Rich families).
Whether Vaughn and Davis families are related depends entirely on which Vaughn family and which Davis family is being discussed. These are very common surnames and many people using the Vaughn surname are not related to each other, let alone to families using other surnames. The same for families using the Davis surname
Condrick is a common surname or family name... As far as a word there is no such word in the English language outside surnames or family names as in Mr. Condrick was our English teacher. Even looking through my Antiquated Words dictionary which includes obscure and words no longer in use. Nor could I find the word Condrick in German with the exception of surnames or family names...