Greetings,
EndNote does not currently have built-in functionality which would automatically suppress a name suffix within your formatted in-text citations - this is a great suggestion, and I’ll be certain that it has been logged with Development. I can suggest a couple of workarounds, but the easiest solution would probably be to not include the name suffix within your EndNote library record, remove field codes from your Word document after final formatting, and manually add the author suffix information to the formatted bibliography at the end of your document.
In terms of semi-automated workarounds:
1. You could insert your citation with the normal workflow, then use the Edit & Manage Citations command to customize the in-text citation to exclude the author information. Along with excluding the author information, you would type the author surname alone within the Prefix: field on this window.
2. We could designate a field within your EndNote library, separate from the author field, to store name suffix information. We could then edit your output style to exclude the suffix field within your in-text citation template, and modify your bibliography templates to include both the Author and suffix fields to always display complete author names.
Please let me know if you’d like assistance with either of the workarounds mentioned above.