If you are operating in same field of the other company, you may not use the trademarked name without prior approval of the owner. If you wish to use the said name, you can obtain NOC from the owner allowing you to associated mark with your business.
If the operating fields are different, choose applicable classes to your business and check if their mark is registered in given classes or not. If not, you can use the mark and also apply for registration.
Here, having consultation with an expert with facts of case is important. Do not reply only on the answers over internet. Facts and case changes the answer as well.
I would recommend not using a brand name already in use as you never know when you or the other company become business giant and it may harm goodwill of one of two.