Amorim's reputation will change if he succeeds in turning the current team he has into something extraordinary. We know how poorly United performed last season; even a slight improvement will be very noticeable. They have some new players, and we will see their performance for this season. Hopefully, the results that Amorim will show are something positive. If not, his career with United might come to an end.
If you noticed, he pressured the board to get him more signings according to reports from several football news, he needed more Premier league proven players that's why most of the players they've signed so far a the ones already in the league that were outstanding for their various clubs last season, that's a first step to improvement but it doesn't guarantee that they'll succeed with that, Amorim still needs to put more effort in training those players to understand what he wants and the way he wants them to play, if things work as planned there's a high chance that Manchester United would do more better than the previous season, if they can finish in the top 6 and try to win a trophy then we'll say they had an impressive season and definitely Amorim's reputation would increase, he'll get more support from the board and fans.