The "mit beschränkter Haftung (mbH)" suffix (German: [ˈɛmbeːˌhaː], "with limited liability") is sometimes added to the name of a firm that already ends in "-gesellschaft" ("company"), e.g., "Mustermann Dental-Handelsgesellschaft mit beschränkter Haftung" ("dental trading company with limited liability"), which would be abbreviated as "Mustermann Dental-Handelsgesellschaft mbH".
In a few states, you must take an additional step to make your company official: You must publish a simple notice in a local newspaper, stating that you intend to form an LLC. You are required to publish the notice several times over a period of weeks and then submit an "affidavit of publication" to the LLC filing office. Your local newspaper should be able to help you with this filing.
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.