Of course there is a command for storing a calibration string.
RTFM, please use calibration manual, page 74, or user manual, page 165:
CALSTR string[,security_code] stores the string in non-volatile memory, maybe secured by the calibration security code, if set. This command is available over the GPIB only.
CALSTR? will return this string.
A calibration usually verifies (i.e. PASS/FAIL) the 3458As 1year limits against external calibrators, like a Fluke 5730A, plus another ' Gold Standard ' 3458A.
In case of the standard reference, for the 10V range, about 10ppm test limit has to be checked, for option 02, this is about 5ppm.
Therefore, for the standard case, the 5730A and the reference 3458A may just manage that level of uncertainty with enough T.U.R. (Test Uncertainty Ratio), but will fail for the latter case, as about half of the uncertainty is needed. That's also valid for verification of the other DCV ranges.
This can only be achieved by using a well characterized Fluke 732B reference, with <1ppm uncertainty, and a Fluke 752A ratio standard, < 0.5ppm uncertainty, or a JJA system, especially, when additionally a precise adjustment (10V, 10kOhm) to 24h specification shall be done. This equipment and uncertainty grade are available only in higher grade laboratories, like Keysight Loveland.
Good information about this subject can be found in the Fluke AN:"Calibrating the Agilent 3458A DMM with the 5730A Multifunction Calibrator" , and on Keysights metrology youtube channel "Keysight Calibration & Repair":
https://www.youtube.com/channel/UCG8BVoXwdZqz-PlZxeO56Twwhich can also be found as documents on the Keysight training site:
http://www.keysight.com/main/facet.jspx?t=79831.g.1&cc=US&lc=eng&sm=gFrank