What is your choice for primary key in tables that represent a person (like Client, User, Customer, Employee etc.)? My first choice would be an social security number (SSN). However, using SSN has been discouraged because of privacy concerns and different regulations. SSN can change during person lifetime, so that is another reason against it.
I guess that one of the functions of well chosen natural primary key is to avoid duplication. I do not want a person to be registered twice in the database. Some surrogate or generated primary key does not help in avoiding duplicate entries. What is the best way to approach this?
What is the best way to guarantee uniqueness in your application for person entity and can this be handled on database level with primary key or uniqueness constraint?
As mentioned above, use an auto-increment as your primary key. But I don't believe this is your real question.
Your real question is how to avoid duplicate entries. In theory, there is no way - 2 people could be born on the same day, with the same name, and live in the same household, and not have a social insurance number available for one or the other. (One might be a foreigner visiting the country).
However, the combination of full name, birthdate, address, and telephone number is usually sufficient to avoid duplication. Note that addresses may be entered differently, people may have multiple phone numbers, and people may choose to omit their middle name or use an initial. It depends on how important it is to avoid duplicate entries, and how large is your userbase (and thus the likelihood of a collision).
Of course, if you can get the SSN/SIN then use that to determine uniqueness.