Within a unit yes, you cannot change targets once you've allocated shots.
With multiple units though, you can shoot with the first unit, see the result then shoot with the second depending on what's left, even in overwatch.
But reread the FtGG rules.
When an enemy unit declares a charge, a unit with this ability that is within 6'' of one of the charging unit's targets may fire Overwatch as if they were also targeted. A unit that does so may not fire Overwatch again this turn. Xenos 2 PG 48
Now look at the Charge Phase.
Each time a charge is declared against a unit, the target unit can immediately fire Overwatch at the would-be attacker... Overwatch is resolved like a normal shooting attack and uses all the normal rules..." Core Rulebook PG 182
The rule itself says that if you use supporting fire, you may not fire overwatch again this turn. If you look at the Charge Phase rule, is says it is resolved like a shooting attack. So just like in my crisis suit example above, you've already declared where those shots are going. Whether or not you've hit the target or not doesn't matter. You've still declared it.
The Risk - I can't shoot Overwatch again this turn.
The Reward - I get to add my Overwatch strength to the unit beside me.