What Do You Call Name Suffixes Like Jr., Sr. Esq, Etc?

Yes, they are called 'name suffixes':

'A name suffix, in the Western naming tradition, follows a person’s full name and provides additional information about the person. There are academic, honorary, professional and social name suffixes.' (Wikipedia, granted).

'Jr.' and 'Sr.' are personal name suffixes.
'Esq.' is a professional name suffix.
'MBA' is an academic name suffix.

Rats. I was hoping for a one word term. I guess that's my so-called luck.

designation

They are called a "suffix". These include suffixes like Jr., Sr., III, etc. and do NOT include "professional suffixes" such as MD, PhD, etc.

(I'm designing a contact database and am studying the names of these fields, etc.)

rAllcorn

Richard A. Allcorn

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In doing some research in names, for a contact database project I am working on, I found the following:

Sample name:

Dr. John P. Doe, III PhD.

prefix=Dr. (the professional, or courtesy title: Mr., Mrs., Dr., Master, Miss, etc.)

first name=John (Christian name, given name, prename, forename)

middle name=P. (in this case, an abbreviation, but usually an added or secondary name)

last name=Doe (Family name, surname ... sometimes the maiden name if not married, married name if married)

suffix=III (the "name" designator, often used to differentiate from another with the same name - Ex: Jr.)

professional suffix= PhD. (often a professional title will follow the name, and suffix where applicable -2 spaces after)

Generally, the "professional suffix" is not used except in signatures, or professional communiques where the professional position of the individual is used in the name to carry extra "weight", as it were, in influencing the reader.

- DEFINED BELOW -

suffix
Noun: A "suffix", in the Western naming tradition, follows a person’s full name and provides additional information about the person. These are usually Jr., Sr., III, etc. and are directly related to the name and the identification of the individual. See "professional-suffix".

professional-suffix
Noun: A "professional suffix" generally follows a person's full name and suffix, with an additional designation that may refer to a professional title, an academic title, etc. Some examples are: PhD, MBA, GRI, etc.

rAllcorn

Richard A. Allcorn

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my father inlaws name is Frank Martinez Castillo, my husbands name is Francisco Castillo Jr., because my husband is not really a JR, how would i name my son if i want to keep the name Francisco??

Francisco Castillo Jr. Jr. or Francisco Castillo III ?

Tittle

also called post nominal letters.