A formal definition of communist economy, among other important attributes, posits that tools of production are owned by the state/community, NOT by individual. Even if that individual built said tool of production all on their own.
In practice, it means that said state implementing communist economy requires a mechanism by which an individual who created tools of production is compelled to relinquish them to the community ownership.
- You don't like crappy communal hammers. You make your own fancy hammer. BZZZT. Not your own. Community now owns it, not you. You can go back to using crappy communal ones.
OK, the valid criticism in the comments is that hammers don't count as real "tool of production" that a communist economy would require to be community owned. Rather than arguing over what is and isn't a tool of production, let's take an example that would certainly fall under that category, because it already practically fell under that category in USSR (which had socialism with only partial communal ownership that didn't go as far as real communism is supposed to. In other words, if something was illegal to own in USSR, it would most certainly be impossible to own in real communism).
- You invent a new machine to dig potatoes. You spend couple of years building and perfecting it. You almost never get to use it; since it's a communal tool of agriculture (if your village has 200 people, you get to use it as much as everyone else - that is, 2 days out of a year. If you're lucky, those 2 days are during when you actually dig potatoes). So you're back to using a shovel when someone/everyone else gets to use the machine you built.
In a typical "communist wannabe" socialist states, this result was achieved by the government being effectively a dictatorship (or; at least; authoritarian to a large degree) so they compel such relinquishment with a law (such as Article 153 of 1960 USSR criminal code "Private Entrepreneurship") that's backed up by threat of force from the government (see Dekulakization for more extreme version). Or by simply wink/nod/ignoring smaller tools of production - you could make your own hammer but not your own factory.
But that forceful option isn't available to a form of state that's supposed to be more democratic and/or less forceful, such as proposed anarcho-communism, libertarian socialism, etc... yet fully communist.
As such, how do such ideologies propose to practically address this problem?
More specifically: how would a non-dictatorial communist state compel an individual to stop owning (and relinquish into communal use) the means of production that said individual made themselves on their own time?