Marxists don't understand two things. (1) the value added by the entrepreneur, and (2) the necessity of profit (savings) in order to invest. — Agustino
Whatever it is that Marxists do or don't understand, successful societies require the
function of the entrepreneur -- which is, essentially, a creative actor. A socialist economy would need creative actors as much as a capitalist economy, because perpetually changing circumstances require new solutions.
There are lots of people who perform entrepreneurial functions in non-profit organizations, for instance--almost always in the first few years of the organization.
Let's say that there was a sudden eruption of multi-antibiotic resistant infections, which tended to be disfiguring, disabling, or fatal. New NGOs would be formed quite quickly to address local conditions. Creative actors would lead the search for programatic solutions. Universities would start new labs to research the issue, and there would be a search for technically able scientists who could also think outside the box. The same would go for governments and health companies.
Most of the people working to solve the infection problem would not be in businesses: they would be elsewhere. The same would be true in a socialist economy. There would be inventions addressed to existing or new problems. Creative managers would find fresh solutions to supply chain problems--and so on--PROVIDED that the socialist economy did not operate as a command economy like the USSR. Command economies aren't altogether bad, but I think they tend to be arthritic, and may develop blindness to new circumstances. Capitalist economies can do the same thing, of course, but through different mechanisms. The obsessive drive for ever higher profits, for instance, blinds stockholders to the impending disasters of pollution, global warming, and so on.
Your concern is that entrepreneurs would not be properly rewarded, and as far as I can tell, a socialist economy would probably not adequately reward you for your wonderful new ideas. How creative managers, inventors, other creative types would be rewarded is a question which I do not have an answer for. In some socialist arrangements, they might be very highly rewarded, in others, less so. But "high rewards" is relative.
Most people, it seems, would prefer to make less income, as long as their economic standing compares favorably with others, rather than making 10 times as much, but being the least well paid man in the company. So, if they develop a product worth a million dollars, they might not get $100,000 in reward. Maybe they would only get $10,000. But... that $10,000 would be relatively high, compared to others.