Table with only one column because of many-to-many relationship? Right now I have three tables: person, alias, and person_alias. As suggested by the names of tables, one person can have multiple aliases and one alias can be used by many people, and hence I add a joining table person_alias during the process normalization.

However, the table alias essentially only contains one column (if I do not choose to use numeric surrogate key). In addition, let's say the table person also contains a bunch of other useful information that is irrelevant to the question here.

I am not a bit stuck at justifying setting up the entity relationship map this way. What is the problem that I delete the table alias all together? Or do I misunderstand many-to-many relationship/normalization?
The alias table will save space because you do not repeat duplicated aliases in the person_alias table. 

If in most of the cases aliases are unique, then this won't matter much, but if you have a lot of duplicated aliases (say every second person uses 'Zaphod Beeblebrox' as a alias) then this could save a lot of space. 

However, if you allow a single person to rename their alias without affecting all other (duplicated) aliases, then removing the alias table completely could makes sense. 

You could de-normalize further and store all aliases for a person in an array column in the person table removing the person_alias table as well. But in that case it will be quite complicated to define a unique index that ensures that every alias is unique for that person. If you (almost) always retrieve all aliases for a person together with that person that might be slightly more efficient. 

But if you want to ensure uniqueness of the aliases per person in the database, stick with the person_alias table.