Erika,
     These are the child's Hebrew/religious/Jewish/Yiddish name.  First of all, I say Hebrew/religious/Jewish/Yiddish because they are essentially the same thing.  Whether the name is of Hebrew or Yiddish derivation, it is the name used for religious purposes.  These names may or may not correspond to the secular version of their name, just like in modern times the secular name may or may not correspond to the Hebrew/religious/Jewish/Yiddish name.  Take my own daughters as an example.  Sara Grace has the religious name of Sarah Basha (Yiddish), Alisa Lauren has the religious name of Aliza Lior (Hebrew).  They're just the names we chose.
     In these records you will also notice that not every Jakab is Yakov and not every Simon is Shimon.  I've seen Jakabs given the religious name of Hirsch Tzvi and Simons given the names of Shimson (Samson), Shlomo (Solomon) and Yakov.  :-)
     These names are not found on all Hungarian birth records.  For example, in my ancestral town of Körmend, there are two sets of birth records available on familysearch microfilms.  One set has the religious name, but not the father's occupation or the parents' towns of origin.  The other set has the father's occupation and parents' town of origin, but not the religious name.  So the lesson is to search all record sets, because you might find different information on each register.  In other communities where there is only one register, it may or may not have the religious names.  Sometimes the religious names are on the earliest records for a given town, but that's all.  And sometimes the reverse is true--you might see them on later records, but on the earlier ones.  It's pretty hit and miss.  And if the religious name is included at all, it's usually on birth records.  I've seldom seen them on death or marriage records.
     These names are incredibly helpful for research, but they are not always transcribed.  Maybe capturing religious names wasn't part of the assignment, or maybe the transcriber didn't know Hebrew/Yiddish.  So the other lesson is that it always pays to look at the original record to see if there is additional information there.  Records that were transcribed early on tend to have the least information--the instructions for the project were pretty much just to capture names and dates.  It is now the standard to pretty much capture all the information on a given record--witnesses' names, notations of name changes or conversions, pretty much everything except the midwife's name!  :-)  So again, if the original record is available, it's always a good idea to check it.
     Best,

             Judy Petersen