Different model requirements for POST and PUT
I prefer to keep separate models to be honest. You could have a base abstract ( or not ) model with all the common properties although this is not required and simply adds a third class. Is there a need for it? I'd say no.
There are slight differences between POST and PUT.Neither POST nor PUT require the Id property if you already have that in the PUT endpoint. This negates the need of checking if that Id in URL matches the Id in the model.
Your example does not make the difference visible, but in many cases there are fields you don't really want to update. For example let's say you have a Created and Updated date fields, you would not want to change your Created date via a PUT for example. The more data you have that you do not want to update via a PUT, the more obvious and worthwhile the differences between the models become.
In your case even with those 2 properties I would still create 2 different models, even if they are virtually the same, this sets the expectation on how the API works and creates a clear design in the mind of everyone else who is working on it.