Think about the arguments to cursor.execute that you want. You want to ultimately execute
cursor.execute("SELECT * FROM my_table WHERE name IN (%s, %s, %s) AND id = %s AND puid = %s;", ["name1", "name2", "name3", id, pid])
How do you get there? The tricky part is getting the variable number of %ss right in the IN clause. The solution, as you probably saw from this answer is to dynamically build it and %-format it into the string.
in_p = ', '.join(list(map(lambda x: '%s', names)))
sql = "SELECT * FROM my_table WHERE name IN (%s) AND id = %s AND puid = %s;" % in_p
But this doesn't work. You get:
TypeError: not enough arguments for format string
It looks like Python is confused about the second two %ss, which you don't want to replace. The solution is to tell Python to treat those %ss differently by escaping the %:
sql = "SELECT * FROM my_table WHERE name IN (%s) AND id = %%s AND puid = %%s;" % in_p
Finally, to build the arguments and execute the query:
args = names + [id, pid]
cursor.execute(sql, args)