I disagree that this would be desirable.
First, unless we want people to focus on the user, instead of the content, who posts something should have little or no bearing on anything. Act on whether it's good or bad content (or proposal, or whatever), not on who posted it. The only case where who posts something should be relevant is for moderation purposes, and for that, the display name shouldn't matter; moderators need to have access to historical interactions from the user regardless of the display name used anyway.
Second, people sometimes want a break with a previous name they've used. Maybe they feel it doesn't represent them any longer; maybe they want more privacy than their old display name affords them (for example, changing from their real name to something else); maybe they realized that it could be misinterpreted; maybe they want to use the display name to prominently make a statement; or maybe they have some completely different reason for wanting to change it. In any case, they're changing their display name; certainly anyone who does so should realize that this will change the name their contributions are displayed as attributed to. It won't be a completely clean break if they have interacted with the site in any significant way, but they can still get most of the benefit without having to create a brand new account.
Third, it's potentially complex. Sure, the easy approach is to just show the most recent previous display name until a given amount of time has passed since the change was made. But that just means that people need to change their display name twice in short succession (by choice or by accident) for the old name to disappear. So now we're potentially considering displaying a history of past display names for a period of time. Trying to lay that out well in the UI is bound to be difficult, and of course each such past display name will need to be tracked separately.
Fourth, every once in a while, people actually set their display names to something that is genuinely offensive. (I've seen it happen, though thankfully not on Codidact.) If that happens, it needs to be possible to minimize the exposure of the offensive display name. Displaying old display names, even if only for a period, increases the amount of exposure such an offensive display name gets. If a history of past display names is displayed, not just the most recent one, they could also use that to display a message that would be more difficult to redact. This can perhaps be worked around by allowing a moderator or site admin to redact such a history entry, but now we're piling even more complexity on top of this.
There are probably more arguments against this that I'm just not thinking of at the moment.
Seems to me that it is easier to focus, first and foremost, on the content of each user's contributions.