When can a person be called rich? What is the common definition for economic richness of a person?
When can you say John Doe (hypothetical name) is rich (objectively)?

Strictly economically speaking, no philosophical debate.
There is no commonly-accepted definition. Different countries and different organizations within a country will have different definitions.

For example, the African Development Bank defines the rich to be those with "per capita consumption levels" of >\$20 per day (2005 PPP).

That would be around or below the poverty line in most developed countries. For example, the 2018 US federal poverty line for an individual is \$12,140 per annum or \$33.26 per day.