IBM employees (in line with industry practice)sign an employment contract which clearly gives the company the rights to own the copyright and/or patent rights to everything we create while employed by IBM. The contract does not explicitly cover the topic of whether or not the company owns the rights to our reputations. However, despite the lack of a formal contract it is inevitable that you employer will effectively benefit from any positive reputation you build up as well as be harmed by the negative reputation that you might gain from doing something stupid.
In the software industry we do not normally distinguish between the ownership of the intellectual property rights to exploit a creative work and the ownership rights of the reputation which comes from being involved with its production. The copyright statement with a piece of software will normally state which company owns the copyright, but will make no mention of the individual employees who worked on the product. This is in sharp contrast with the music and film world who normally give careful attention to recording and publishing a list of everyone who is involved in each piece of work. The credits at the end of a movie will normally list everyone who was involved in creating it - not just people with major roles such as the actors, director etc., but also people with more minor roles such as looking as looking after the catering arrangements for the people working on the set.
The reason for this practice is because the people involved are constantly moving from job to job and as result they need a way to provide proof of their portfolio of work. For example if I applied for a job doing the make-up on a new movie and claimed credit for working on the Harry Potter movie, the prospective employer would probably check the credits at the end of the movie and if my name was not mentioned assume that I was telling lies.
Perhaps the software industry should follow their example and find a way to give credit to all of the people involved in creating products. There used to be a tradition of inserting a hidden easter egg into software products to allow the people involved in creating it have the thrill of seeing their names visible in the product. However, this practice was never formally endorsed by the companies funding the product and it seems to becoming much less common recently. However the practice of having a job for life is no longer common and software engineers would benefit from having a way to prove their portfolio of work.