For example, Professor Stephen Boyd - Samsung Professor, Professor Paul Newman - BP Professor
Does it mean said company pays that professor's salary? Does that professor have any obligations towards said company? Who decides which professor gets which company?
Such things are honorific and based on grants from companies that "endow (fund) a chair". That is academic-speak for a fairly large grant that normally is enough to fund a person and probably their research over several years. The funds will be administered by the university and the company may have some (perhaps a lot) of say into who holds the chair, given that they meet other university criteria. Some of the "endowments" are large enough to be perpetual, with only interest accumulation and such being used for disbursement.
Sometimes such things are used as an inducement to try to attract someone with either a lot of promise or a solid research record.
In the better arrangements, the company will have very limited say, but perhaps a veto.
It is a form of advertising and virtue-signaling by companies.
This situation is called a "named professorship." They are not specific to companies.
A named professorship usually is created because a wealthy individual, or occasionally a company, decides that they want the professorship to have that name. It is similar to buying the naming rights to a stadium or a building. Legally, it's typically a donation. Universities also name professorships occasionally just because they think it sounds good.
Being a named professor is an honor.
Does it mean said company pays that professor's salary?
No. In some cases, money received from the sponsoring individual or company is invested and used to pay some or all the salary at a later date. This is called an endowment.
Does that professor have any obligations towards said company?
Usually no. There could be exceptions. Typically the professor is someone with a track record in an area of interest to the funder.
Who decides which professor gets which company?
Not normally. Most Western universities consider it improper for any professorship to be assigned through any process which is not controlled by faculty. That includes named professorships. However, other countries things may be more flexible, and some Western universities there has been a trend towards allowing sponsors to influence hiring.
