Dynamic Data Masking performance overhead
No, there is no overhead involved (not heard of any yet). I have used it in my Azure SQL Database and works like a charm.

Data Masking is a quick solution for data security as you can control the users who can view the data, but on a broader aspect this cannot be the sole security solution.

Please read below links for better understanding:


Dynamic Data Masking (Microsoft documentation)
Encrypting SQL Server: Dynamic Data Masking by Robert Sheldon