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. ' ( Wikipedia , granted). ' are personal name suffixes.
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It's called a "cadence," from the Italian musical term, "cadenza," meaning a closing embellishment or ornamentation.
You'll sometimes see the term on government online e-forms after it's asked you to type in your name.
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What country?
USA.
There's also a heraldic term, cadency, defined as a "systematic way to distinguish https://en.wikipedia.org/wiki/Coat_of_arms displayed by https://en.wikipedia.