This is probably a bug due to respec of the character. Somewhere along the line, the unit for the pet was created and was assigned an unique ID. This unique ID is still stored in your character's unit, but the corresponding pet unit not longer exists in the game. The game, however, will not notice this and will not clear the data and reassign a new pet unit.
A good way to check this is to use the Data Viewer mod (you need to install this). In the Mod Manager window, go to Data Viewer, Characters, expand the character in question, expand Descriptor, expand m_Pet. If it says something like “[Not found] f84df7bb-e93a-4638-b811-3b395ee94b68”, then you have the same problem.
The easiest solution I have found is to do some save editing. As a precaution, create two manual saves - first that you won't touch and second to edit. I won't describe all of the details, this is not really the kind of thing you can do blindly. You will need an archiving tool (such as 7-Zip) and a solid text editor (such as SciTE), because the save game is just a ZIP file with a .zks extension and inside the data is mostly big JSON files.
Find the missing unit ID using Data Viewer. Otherwise, you'll have to try each of the possibly 10+ occurrences.
Extract and edit party.json. You can format the JSON for easier editing, but this requires a command line tool (such as jq), because any web or GUI tool is likely to crash/freeze due to large size of the file (in my case 5 MB unformatted, 12 MB formatted). Inside, find the unit ID.
It should like like this:
"m_Pet":{"m_UniqueId":"f84df7bb-e93a-4638-b811-3b395ee94b68"}
Replace the string value with null:
"m_Pet":{"m_UniqueId":null}
Insert the party.json file back into the .zks file and load the save game. A new pet unit should be generated for you and appear close to the owner.