How can create a table having the name like a^b along with same column name?name?

For creating a table with such kinds of names we must have to use quote character. The quotes can be single or double depends upon ANSI_QUOTES SQL mode. 

If this mode is disabled then the identifier quote character is the backtick (“`”). Consider the following example in which we created a table named ‘select’ −

mysql> Create table `a^b`(`a^b` int);
Query OK, 0 rows affected (0.19 sec)

mysql> Create table "a^g"("a^g" int);
ERROR 1064 (42000): You have an error in your SQL syntax; check the
manual that corresponds to your MySQL server version for the right
syntax to use near '"a^g" ("a^g" int)' at line 1

If this mode is enabled then we can use backtick (“`”) and double quotes (“”) both as a quote character. Consider the following example in which we created the table like the above name with the help of both quote characters after enabling this mode −

mysql> Set sql_mode = 'ANSI_Quotes';
Query OK, 0 rows affected (0.03 sec)

mysql> Create table "a^d"("a^d" int);
Query OK, 0 rows affected (0.21 sec)

mysql> Create table `a^e`(`a^e` int);
Query OK, 0 rows affected (0.14 sec)