Here is the outline of question:
I have a multi member LLC (XXX) that owned real estate which sold the real estate in 2020 and proceeded to do a 1031 exchange to obtain a "like property" during the proper timeframes etc. Now the LLC (XXX) wants to become a new name LLC (named ZZZ). Same members. Just want to change the name to ZZZ. Can LLC XXX become ZZZ if ZZZ was already created and has its own tax id number? NOTE: ZZZ was specifically created for this name change and was documented during the exchange while obtaining a "like property".
It depends on the type of business conducted by the LLC, as well as the laws/rules of whatever state that LLC is registered in. For changing the name with the IRS (once done/approved at the state level) see https://www.irs.gov/businesses/business-name-change
Basically, at the federal tax level a Partnership and Multi-member LLC are somewhat the same thing. So the requirements for a Partnership as indicated on that website, may apply. Also check out the link to publication 1735 on that web page to help you determine if you need to obtain a new EIN with the name change.
Your LLC was formed under state law and the name was registered when organized. You need to have the named changed at the state level first.
Then you can change the name at the federal level based on your facts.
See the attached IRS link noted in @Carl response.
If you are sending in a letter, then I recommend you send it certified mail return receipt requested.