It does not matter if the LLC at the end of a company name is in capital letters or lower case. I have seen it both ways. What is important is that your company structure is known to the public. I have even seen logos that do not include LLC, PA, PC, Corp. in them
When documents are signed or when the formal name appears in legal documents or on a public website, include the llc or LLC designation.
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Your question is really more one of grammatical style than a legal one. From a legal perspective, it really doesn't matter, as long as it is there. From a style perspective, it's an acronym, and acronyms are almost always capitalized. You certainly don't HAVE to follow that rule, and this is particularly true when designing a logo or letterhead, where artistic style often outweighs grammatical style.
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You don't need to use upper case letters for the abbreviation "LLC," and for your trademark (including your logo), you don't need to use the abbreviation as all, as many companies don't, because it's not a very aesthetic addition.
However, when any officer or member of the corporate entity is signing any document on behalf of the entity, they should always do so using the full legal name of the entity.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.