While you sound like you're on the right track, your logic is a bit jumbled.
First, you don't "trademark" names, logos or the combination of them. You use names, logos, etc. as trademarks, thereby acquiring trademark rights in them. You can then register those rights with the Trademark Office. The distinction is important because you may already have sufficient trademark rights -- albeit not registered rights -- to enforce against the infringer.
Second, your abandoned application, if I understand correctly, sounds botched to me. You should have a qualified TM attorney handle any future filings for you, in my opinion.
Finally, patent infringement, while a bigger bite to take, can be far more powerful a weapon in the market than trademark actions. Under the former, you can stop the infringer regardless of how he brands his product, while under the latter, you can only stop infringing branding.
If this is a true business, why not protect it properly and speak with an attorney about your matter. In the end, it's almost always more cost effective to have an attorney handle enforcement from the outset than it is to try to do it piecemeal yourself.