Your name must be unique, and not deceptively similar, to any other trademarked name or business. It is also required that your name not be used to intentionally misrepresent the products or services you offer. For LLCs, nearly all states will also require you to add a signifier of your limited liability status, such as "LLC" or "L.L.C." to the end of your company's name. You may be able to operate under a name other than your formal LLC name by applying for and using a dba.
LP, Limited partnership: a partnership where at least one partner (the general partner, which may itself be an entity or an individual) has unlimited liability for the LP's debts and one or more partners (the limited partners) have limited liability (which means that they are not responsible for the LP's debts beyond the amount they agreed to invest). Limited partners generally do not participate in the management of the entity or its business.
Oregon For private corporations it shall contain one or more of the words "corporation", "incorporated", "company" or "limited" or an abbreviation of one or more of those words; shall not contain the word "cooperative." For non-profit corporations there is no specific requirement except the name cannot imply a purpose not dictated in its articles of incorporation and cannot contain the word "cooperative" or the phrase "limited partnership." Oregon Revised Statutes 60.094 for Private Corporations; ORS 65.094 for Non-Profit corporations
With the proper planning, limited liability companies can exist for generations. S-Corps continue to exist even if the owners or majority shareholders leave or pass away. C-Corps continue to exist even if the owners or majority shareholders leave or pass away. Non-Profit organizations and institutions survive after their directors leave. Sole Proprietorships do not exist when the owner quits or passes away.
Where the equipment you use in your business was acquired as a gift, you may report your estimate of its current market value on the Business Property Statement (that is, what you think it would sell for in the open market place). Enter that estimated value in the most current year's cost line and add a note indicating that the entry is an estimate.