In short: "Yes!"
In medium-length: "Don't do that!"
In long form:
There are at least several issues with legal ramifications that you should consider:
Unauthorised use of trademarked - or otherwise protected - names: There are companies that sue for such use as a matter of principle, in order to protect their trademarks - in some countries they are actually required to do so, lest they set a precedent. While there are fair use clauses in the laws of most countries and you may win a court case, such companies can throw what - to most people - is unbelievable amounts of money to their lawyers and cause you lots of trouble just by suing. Can you compete with that?
Offensive use of their names: The trademark law is usually more tight and companies prefer suing for trademark infringement, but should they chose so, they can also sue for offensive use of their names. For example, if in your game a character working in company X is routinely overworked and harassed by the superiors, the company might find grounds to sue for defamation.
Embedded advertising: In some countries you are not allowed to do anything that might be received as covert advertising, sometimes depending on the target group of your own product. For example, you may not be allowed to have any Real-Life products or companies in a game inteded for young children.
That said, I am not a lawyer, and you should probably ask one with expertise on trademark and related issues for an answer with more weight.
Or you could just avoid using such names in your game. Keep in mind that paraphrased names or photographic descriptions can also get you into trouble in some cases - for example having a software company named "Minisoft" and presided by "Gill Bates" is pretty obvious.