The tec rules of a primary Key are as follows
The PRIMARY KEY constraint uniquely identifies each record in a database table.
Primary keys must contain unique values.
A primary key column cannot contain NULL values.
Each table should have a primary key, and each table can have only ONE primary key.
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So technically there is no rule against it, BUT Primary Key is usually auto incremental (each new entry is given the next number) which does not work for names, this is why Primary Key is usually integer and not varchar, So doing this you will need to make sure Auto increment is turned off.
Also if you do what you suggest it could cause problems latter on if someone decides to change a name, or expand the table and mess up the Primary and render the table broken. I wouldnt do it.