The names might have appeared in any order or only one of the two, the same for father's name.
The first person might have been known as Chaim-Ber son of Yudka-Leyb in one document, Chaim, son of Idel in another, etc. Just an hour ago I was looking at someone's record in a census, where only one of his given names was used and his father's name was listed as Yuda-Leyb (same as the person you are asking about). His death record 40 years later in another locality had his name written as <both names>, son of Idel-Leyb. It's obvious it's the same person but was using slightly different Yiddish name, based on the Hebrew Yehuda. Ber might have been written as Berko, Dov, etc Some of the birth records, where my 2x ggmother is listed as a mother, her name is written as Sheyna, others as Sheyndlya. I guess depends what the person who reported the birth felt like saying that day.
Also, the terms "reb" or HaLevi wouldn't be listed in the vital/census records, just on the matzevah.