As Ralgha stated, this kind of callout would be included in the SOP. A couple I found in searching were the NBAA (same in their helicopter procedures by the way) and Angel Flight NE, as well as some generic CRM guides. The FAA Instrument Procedures Handbook also mentions altitude callouts, suggesting something like "two to go" and "one to go" (in thousands).
The NBAA includes this specific phrasing:
The callout is to include the altitude vacating and the assigned
altitude i.e. “Six thousand for seven thousand” or “Flight level
three-zero-zero for two-niner-zero”. After the PF makes this call, the
PNF will verify and validate the call by stating “check”.
This Flight Safety Digest mentions that USAir used to use the "two to go" and "one to go" phrasing, but opted to change this for the same that the NBAA uses. The new policy has the pilot flying make this call, since they are in control of the climb, and makes it more clear what the final altitude will be.
The Flight Safety Foundation went in to a bit more detail about the "why" behind the callout. They mentioned that in their observations, the callout was sometimes not done due to workload of other more important things going on in approach/descent. They explain the benefit:
This is not to suggest that the 1,000-ft callout is trivial. On the
contrary, it ensures that both pilots concur about the altitude
target, directs the attention of a flying pilot who might be
distracted back to the impending level-off and draws both pilots’
attention to what the autopilot is supposed to be doing.
Another resource that suggests the important is a report of an aircraft overshooting its altitude by 600 feet because the callout was missed. This report is in the ASRS database, report number 317750.
I also found it referenced in this book about communication. They didn't really comment on it specifically, but used it as an example of how communication is critical. Specifically, the more exactly the terminology is defined, the more clear the communication will be.