Inserting a record into a MySQL table using PDO
No, it's not vulnerable to SQL Injection, as you use prepared statements, and you use them correctly.

If you don't have any CSRF protection it is however vulnerable to XSS because of the echo (and of course CSRF), but I'm assuming that that's more of a debug statements.

Misc


You don't really need the variables nameone and nametwo. One-time variables are only useful if you need to give them some name to increase readability.
You shouldn't use mysql_*. So if you want to set the character set you should use PDO (you can also pass it as optional MYSQL_ATTR_INIT_COMMAND parameter when initializing the connection, see eg here).
try to be consistent with your names (nome vs name).
use camelCase to make your names easier to read (nameone -> nameOne).