So is this our Elizabeth Emily/Emily Elizabeth Gell? No mother's maiden name given.
Births Mar 1874
Phillips Elizabeth Emily
Droxford 2c 115
Looks as if the Gells didn't marry, but she took his name.
If this is the case, it could be that John Gell wasn't Sydney's father and that is why he reverted to Phillips when he was older, but was Elizabeth's father, so she kept the name.