Are you aware that JosepSmith15/01 is not guaranteed to be a unique value? It's entirely possible, though rare that you could get two different individuals with same first name, last name and birth day/month.
An auto-entered serial number is what I would recommend that you use, but generate it in a separate table related to this table. In that table, you can limit records to one record for each unique value in this combined names_Birthdate field.
Use a text field in that table for holding the JosepSmith15/01 data. Set up separate fields in this new table for first, last names plus a date field for the Birthdate and define an auto-entered calculation on the text field to combine them. This allows you to set a unique values, validate always setting on that field so that you can import all of this same data into that field, but the validation rule will filter out the duplicates and only permit the import of one unique instance for each combination of names and birthdate. If you enable auto-enter functions during the import, an auto-entered serial number in this field can then function to give each individual a unique serial number.
You can then link this new table to your original data by the names/birthdate combo fields to make that serial number value accessible to the records in the original table.