If a company misses to name an inventor in an already filled patent application, and the inventor requests to be added, is she obliged to assign rights to the company as a prerequisite for having them add her name in the list of inventors in the patent?
Here we assume she is a true inventor and can prove it. If the answer is no, but the company insists, what could she do? If the answer is yes, why is then naming an inventor and assignment of rights correlated?
The answer to your primary question as I see it is that inventorship is completely determined by who actually conceived of the claimed invention and is a separate issue from any assignment. If you invented something that is claimed you are required to be shown as an inventor if an application is filed. You might have run over a fellow employee in the parking lot and be in jail, but if you are an inventor you need to be named.
You typically sign over any inventions you make in the duties of your job to the company you work for -- this is usually written into your contract, unless something is written as part of local laws.
Hence, the signing of the form that the patent belong to the company is a pro-forma signature, as they have recourse if you refuses to sign it anyway.
If you contract does not state that your work they paid for belong to them, then that is a legal blunder on their side, unless there is case law in the country and local laws which states otherwise.
In the US is is very normal that all work you are doing in the cause of your job duties or using resources provided by your employer (such as computers, email accounts etc) belongs to your employer.
Asking you to sign the associated patent form is quite normal, and usually without drama.
