Do you need to include “LLC” in your logo and advertisements as long as it is included in the legal name?
No. The letters “LLC” do not need to be in your logo.
However, I would ensure that all your legal documents–meaning contracts, leases, purchase orders, etc.–use your full LLC’s legal name, and that you sign any documents in your capacity as a member of the LLC and not personally.
In other words, you should sign as “Jenny Smith, Member XYZ, LLC.” and not merely as “Jenny Smith”.