I was looking into the 1848 Appleton's Guide, the 1851 and 1854 American Railroad Guide, and the 1868-1977 Official Guides recently and noticed that there were several Southern Pacifics that were listed as being operated by or leased to Central Pacific.
I do not have an answer, but Southern Pacific of California, Southern Pacific of Arizona and so forth might have been similar to the way many western "Railroad Companies" were built and owned by UP (for feeder branches).
If CP did start and own SP, then just like D&RGW bought SP and took SP logo, maybe CP started/owned SP and then later took SPs name to "get around" restrictions in the "Pacific Railroad Act."
Doug vV