I have a Personal NPC plugin when a bot kills someone or is killed there is no inscription, can I somehow add it myself or should the plugin developer do it?

Look in the DeathNotes.json file, under the "Names" block. There, you see a list that is dynamically updated by the plugin of entities that kill or are killed. Do you see your NPC there? If so, you should be able to add a message block to the "Death Messages" (see above in the same file) to include your desired output.