Name on baptism record different from known name.

How prevalent was it in the mid-1800’s for a person to be known by their middle name versus their name on baptism records? I have been unable to find a baptism record for my wife’s great-great grandmother Bridget O’Dea who reportedly was born in April 1853 and was from Galway.— even accounting for the possibility the year of her birth was off 1 or 2 years give or take. We believe she came from Moycullen. (U.S. census records for the District of Columbia in 1870, after Bridget emigrated, show that she and her husband were living with a Luke and Bridget O’Dea, who various records show were from Moycullen parish.) I have scoured the Moycullen parish records as well as parish records from Rahoon and other adjoining parishes. My best guess so far is that Bridget’s baptism was recorded using , her middle name, Catherine, as there was a Catherine O’Dea born to John O’Dea and Anne Bane in April 1853 in Moycullen. I also believe, based on other records that this John O’Dea was a first cousin of Luke O’Dea. I appreciate if anyone can offer any insight on this. Thank you!