The most obvious and important trade marks to register are the name of your game/app together with any logo you have adopted. It is wise to get specialist advice both in terms of the marks you select and the precise goods and services you decide to protect.
In addition to registering your core brand. As your business grows, or other symbols become more closely associated with your business, it is worth conducting a regular review to identify other possible trade marks to register.
For example in the gaming industry, consider registering the name of your new DLC or the subtitle of a new game (such as WRATH OF THE LICH KING or THE WIND WAKER), key character names (such as PIKACHU, or LARA CROFT) and key hashtags and phrases to ring fence social media use such as the famous IT'S IN THE GAME catchphrase which EA used in the intro for numerous sports titles. This protection can even extend to the shape of a physical product, e.g. a uniquely designed console such as the Nintendo GameCube.
Like all trade marks, these marks need to be distinctive and not descriptive of gaming goods and services. This means that a gamepad emoji or CONSOLE in relation to video game apparatus in class 28 are not available for registration.