The desktop app does have contacts. It's in the Wallet/Contact menu where you can add a contacts (I.e just mean add an address and give it a name). You can then enable the contact tab in "view" menu
You're right! Sorry about that. The mobile version is inferior to the desktop one; it is missing some features like testnet, coin control and message signing and it is also the case for contacts. As I wrote above, you can request that feature on their Github. I highly doubt that it will be added anytime soon since there are other important features missing.