What do you do if another family member lists an ancestor with the wrong name?
Here is the link to the Knowledge Article to correcting information of a family member Correct a person's vital information in Family Tree • FamilySearch.
I'm going to take your question at face value and assume the ancestor is the right person and all other information is correct and this really is your ancestor and that only the name is "wrong."
You go through a series of questions:
Why do I think this name is wrong? Have I always known this person by a different name which actually was not his name? Is it just a variant spelling? Do I have sources that show the "correct" name? Does the person who recorded the name have sources that show the "wrong" name? Is this a birth name and I have a later legal name or vice versa? Is this a pre-emigration name and I have a post-emigration name or vice versa? Has this other family member used a nickname instead of a full name? Or used a married name instead of a maiden name?
Then you message this other family member and ask why he or she entered the name that you disagree with using. If there is legitimate support for both names, you enter one under Vitals, the other under Alternate Names, put on sources for both names, and under the Reason Statements explain what each name is. It really does not matter much which name is in which section other than when displaying pedigree charts. The program uses all names in all program routines.
I ran across an interesting situation recently in which a woman used three names in her life:
Then on her gravestone is found her married name of Karoline Maria Olsen.
All four names have been entered on her Family Tree profile because all four are correct.