By rules, no.
But in the 5e games I've run, even the ones that fell apart early on, I told the players they could change stuff early on if they felt it wasn't v working.
In my current campaign, the sorcerer decided in session two he wanted sleep as a spell. The elf ranger decided he was from a different elf clan in a different country.
In a previous campaign the devout desert fighter (but not a Paladin) decided at level two he really wanted to be an actual paladin.
In each case, the PC was fundamentally the same character just more in tune with what the player wanted.