Is it illegal to use the title of a movie by someone with mainstream credibility for a record company?

This is the sort of trademark question I like to deal with. You should speak directly with a lawyer to help you work on this, because the specifics of the name and of your company will make all the difference. In naming your record company, you should be choosing a name that can be registered as a trademark. The name of a famous movie may or may not be able to be registered as a trademark for your record company, depending on many factors. There may also be trademarks already registered in the movie name by the movie company, and these may interfere with your use of the name. For example, when a famous movie is made, although the name of the individual movie may not be be qualified for trademark, trademark might be registered for many associated products. That is why you need to work directly with a lawyer.

A title can not be copyrighted or trademarked so no one can claim exclusive use of it. However, you want to avoid using any title or series of words that are so closely connected with a producer, director, or actor that people get your company and the movie confused. You can't use the publicity/good will/name recognition generated by the movie to promote your own company.