That is a correct impression. A name, date, and associated place, with all three assumed to uniquely identify an individual in most cases, are required to perform the ordinance. Most typically, that's a birth name and a date and place of birth, date and place of death, or date and place of marriage.

If it turns out that there were two people with the same name born in the same town on the same day... well, the angels will help figure that out later.