Non-EU citizens are in general not allowed to work in Germany without a valid residence permit.
A residence permit is restricted to a certain employer for the first two years of employment. The name of the employer and the job title at the company are in this case mentioned on the permit, e.g. employment only allowed as Scientist at the European XFEL GmbH. Should one change jobs during this time frame, the imposed restriction on the permit needs to be changed to the new employer and new position at the local immigration office. Together with the supporting documents you receive from our side, it is a rather uncomplicated matter.
After two years of employment in Germany, this imposition ends, meaning employment is allowed completely regardless of the employer and position and no further action would be needed.