Not necessarily.
Suffixes such as Jr., Sr., II, III, or IV may appear as part of your name on your identification or on the document you are signing. However, Florida notary law does not specifically require your handwritten signature to include your suffix simply because it appears on your identification.
For notarization purposes, the Notary must have satisfactory evidence that you are the individual described in and executing the document. Online Sunshine
If the document specifically prints your name with a suffix or provides signing instructions, you should follow the requirements provided by the document's issuing or receiving party. The Notary cannot advise you to change the name on the document or determine how another organization requires you to execute it.
If the name on your document differs significantly from the name on your identification, contact us before your appointment so we can determine whether satisfactory identification can be established.