Citation :when people are married, the bride and groom (and their parents) use the "First name" they are to be called by, or that they actually use. Whether or not it's the first name on the baptism register is irrelevant.
I think all church records would use the official name given at birth, even if the person used their second name in every day life. For example, if a woman’s name at baptism was registered as ‘Maria Antonia’ her marriage record would show the same name, even if she was simply called Antonia by everyone. In certain church records, the baptism record of the woman would have a note added next to the name when she got married so as to have coherent records, I assume. The names would therefore be the same. But maybe it depends on the parish?
But it is strange that she was called Eliza and none of her names were similar. What were the other names?