I loved a old game company, however they have gone bankrupt along time ago. I was wondering what happened to its name etc. Is there a way to find this out?
Normally the rights of the name is stay with the original founder or publisher. So if you know the name of the bankrupt company you have to contact the original founder or publisher they worked for. But if the company was success sometime apart from that they finally gone bankrupt, it going to cost a lot of money if they willing to sell at all.
Basically you can’t buy only the name, formally you have to buy the bankrupt company and it remaining debt I guess. 
Cheaper if you found your own company with it own name.