Is ity correct to put a comma at the end of a persons name when writing a sentence?

It entirely depends on where the name fits into the structure of the sentence, as it would with any other noun. A person's name is just a noun!

For example:

'David Brown is my cousin.'

'David Brown, who is my cousin, lives in Canada.'

'The David Brown who is my cousin lives in Canada; the one whom you met yesterday is not a member of my family.'