They change their names, or at least what they go by.
My first problem with this was the girl known in my Brown family as Ethel, who in her first census is called Kattie E., is in her second as Catherine E. (not that different...), so I'd always called her Catherine Ethel "Ethel" Brown. But then her sister Alice (in a letter) comes out with this one: Catherine Ethel Elizabeth Brown. Okay, that's a solution, add another 'random' name just to confuse the issue. This sister Alice is listed in every census as a young person as "Sarah A.", but otherwise seems to have never used the name "Sarah" at all.
It is extremely common to see a child go by one name in one or two censuses and then pop out with a new one for the rest of their lives. Most frequently they are going by a middle name as a child and then as adults they 'revert' to their 'first name', though the whole idea of a 'first name' doesn't seem to have really been important. These people lived at a time when such things as birth certificates did not exist and names could be changed readily.
I see them all the time: Cleo William/William Cleo, Raymond Bert/Bert Raymond, etc. used interchangeably to the point that you can't even tell for sure what they went by, which is part of the point.
I came across another example today. Young Edwin Capps is listed with his parents in Tahlequah County, Oklahoma in 1910 and 1920, but come 1930 and he's married and on his own and he's suddenly Edward! And it apparently stays that way, as it is the name on his tombstone, though he obfiscated the whole thing with Social Security by going as "Ed".
One of the most frustrating ones was a girl who is clearly listed as Elizabeth Alice or E.A. in her father's Civil War pension file, but on subsequently (and on her tombstone) her name is given as Alice Malinda. And you can see the lack of birth certificates created problems: the family bible was considered (for purposes of these pensions) a legal document. Elizabeth Alice/Alice Malinda's father's name was Horton Cox, but his uncle Horton Cox actually died (of disease) during the Civil War. His wife had to reproduce the children's names from the Bible record and when she misspelled one she nearly lost her pension.
"in and for said county [Greene Co., TN] Personally appeared Nancy Cox widow of Horton Cox and makes oath that this only explenation she can give in regard to the discrepency in the name of her Second child named in her decleration for pension is she is no schollar herself, and did not know how the name of sd child was written wither in the original decleration or Suppemental affidavit she first gave the name of sd child to the person who made out her decleration did not know how he spelt it, and when her Supplemental affidavit was made up she handed the person who made it up her family Record and from that the names of the children was taken, and on now being called on for this explination she has the name cearfully examined, and find it Spelt Manday which is the way the father of said child did Spell it as he did write the names in the family Record the affiant further swers"
I do like to know what they 'went by', but the practical problem is how to refer to these people so that other people, other researchers, have some idea who you're talking about. Someone who came across the records in the later half of her life might never make the connection between Alice Malinda and Elizabeth Alice.
Generally, I steal Sarah Alice "Alice" Brown Wiley's solution and list all the names. It gets long sometimes, but at least it's (somewhat) clear.
So, some 'stand outs':
Elizabeth Alice "Alice" Malinda Cox
Nancy Matilda "Tildie" Ellen Pierce
Catherine Ethel Elizabeth "Ethel" Brown
Laura Pearl "Pearl" McRae