As far as I am aware the names Alice and Agnes are usually not interchangable.
People often used their middle names rather than first names, so for example, Mary Agnes and Agnes Mary, or just Mary or just Agnes, may be the one person.
But if her birth certificate says her name is Mary Agnes, but her baptism record says she is Alice, then you might be looking at two different people. Are parent's names given on both birth and baptism records, and if so, are they the same?
I suppose it might be possible for a person to be given a name at birth or baptism and go through most of their life using another name, and die with that name, But when they are born/baptised I can't think why they would be given two completely different names. Were the family Roman Catholics? I know nothing about these things, but might she have been given a different name for some religious reason?
You really need to look at names of parents.