Unless there is any PII associated with the pseudonym, there is nothing specifically in GDPR that says you can’t or shouldn’t do this so long as it’s not information that can identify a physical person. Note that being able to attribute multiple pieces of data to the same anonymous person does not necessarily identify them (and it’s important to not accidentally do so):
It’s important though if you e.g have multiple products to use a _different_ pseudonymization (hash salt or whatever) otherwise you run the risk of storing data linking too much data on a user thereby de-pseudonymizing them in the worst case even though no individual app does. Having a users behavior across multiple applications could pose such a risk in extreme cases.
Edit: I think it's important to separate "hashing" and "hashing". A properly hashed identifier uses a salt that is generated on the client, so that it can't be used to identify the user. basically: the first time the app runs, you generate a random salt which is only stored on the client, and NEVER sent in telemetry. Anything you would like to transmit over the wire that would risk identifying the user (E.g. a computer name, mac address) you hash with this local salt. This way no one can try to go to the database on the server side and try to match any data e.g. check if the hash abc123 matches the computername jimbob bcause hash("jimbob")= abc123. Just sending hash(MacAddress) without a local random salt would NOT be properly pseudonymous because an attacker on the server side could ask and answer the the question "Does this come from the address macaddress?".