In MetaMask Mobile, you can add dapps to a 'favorites' list. Start by tapping the three vertical dots in the lower right, and selecting a 'New tab':
Upon opening a new tab, you will be redirected to the Browse window where you can search for the dapp that you want to favorite. When you've found the dapp, tap on the 3 dots menu at the bottom right again; you should see an option to Add to Favorites:
- Tap on Add to Favorites
- Update / add a name
- Tap Add
Please note, to find your Favorites, you would need to tap on the 3 dot menu at the bottom right, and tap on New Tab, as described earlier.