Yes it would be a smart idea to run a trademark search (copyright only applies to original works, not names). The last thing you want to find in your mailbox is a cease and desist order. When conducting afor existing trademarks, keep in mind the standard that the USPTO and courts use – the likelihood of confusion standard. In essence, if a consumer would be confused as to the source of your product then there’s a good chance for an infringement.
If you want some legal advice regarding your IP rights feel free to stop by. Our community of IP lawyers will conduct a comprehensive trademark search for free! Good luck.