ENS is not currently deployed on Gnosis Chain it is only on Ethereum and some testnets, however there are ways applications can use ENS services to display names. Nifty.Ink is an example application that uses ENS names to identify artists on the platform.
This article by Makoto Inoue describes a simple method to get an ENS address on mainnet and display on GC.
How to Support ENS for Multi-Chain Dapps
In addition, a secure off-chain data retrieval method called Durin is in development which will allow users to access a “Gateway URL” which retrieves data from the specific chain.