Can I use another companies name in my sub domain

I'm no lawyer, but I am pretty sure you can name your sub domain what ever you want. Domains, especially .com, .net, .org names will run into legal trouble. Facebook has tried suing companies that start with "face", I've read. I wouldn't worry until you make your first million dollars, though.

Trademark in domain name will get you trouble. But for sub domain it is a bit tricky.

If you still have other options, say putting the company name in URL which is safe, don't go the sub domain way.

The legal question is whether doing that would be trademark infringement. Answering that kind of question generally requires some details and you don't provide any at all, not even the country you are in.

The answer is almost certainly no, it is not legal. The reason is that using a company's name in your subdomain would lead people to believe there is a relationship between your company and the other company when there is not. This would mislead consumers and the one of the primary purposes of trademark law is to prevent consumers from being misled.

If you did that, you would get nastygrams from lawyers of the respective companies demanding that you stop.