Don't do it that way - it will confuse things, and leave you open to an SQL injection attack.
Instead, use a parametrized query - it isolates the Tamil from the SQL command and means it should just work:
Instead of:
SqlCommand cmd = new SqlCommand("INSERT INTO table VALUES ('" + textboxName.Text + "')", con);
Use
SqlCommand cmd = new SqlCommand("INSERT INTO table VALUES (@NAME)", con);
cmd.Parameters.AddWithVAlue("@NAME", textboxName.Text);