A CNAME-record cannot exist with any other records for the same name, because a name cannot both be an alias (CNAME) and something else at the same time.
From RFC1912 section 2.4:
"A CNAME record is not allowed to coexist with any other data."
If you try to create a CNAME-record for the name of the zone itself, you will always encounter this conflict because a zone always has at least a SOA-record and typically one or more NS-records with the zone name:
Instead of the CNAME-record, you can setup an A-record pointing directly to the IP address of whatever server the aliased name is pointing to.
Or you can use an ALIAS-record which is similar to CNAME but doesn't have the problem mentioned above.
While certain other DNS servers may allow you to configure such a CNAME-record, it is still an error to do so.
The results of this are unpredictable, and often causes serious problems because in some situations the CNAME-record will override other critical records at the zone root level - for example hiding the NS- and SOA-records.