I know about scholarships given my position at my kid's club, parents feeling comfortable with me to ask for help and coaches/admins trusting me with information when they need help. There has been a previous discussion about this on here - pretty lengthy one. Some clubs send out spreadsheets showing who owes fees. If at the beginning of a season, the spreadsheet shows a kid has a balance of "$0", then they can deduce the kid was sponsored - given who the kid is and who the parents are. Wont get into morality or if clubs/teams should do that, but that is how many parents on clubs know if a parent is sponsored or not. Most teams/clubs I have dealt with dont do that for a plethora of reasons.
As far as donations go I have seen, at various clubs, people giving a general donation to cover scholarships. The money is accounted for properly. Nothing stops anyone from donating the money. I've seen people donate anonymously for specific players - most likely family members. I seen families at clubs pay for: classmates fees, kids that go to their church, athletic kids they found in random places (MX leagues, Rec Leagues, Park,etc). I've seen coaches donate back salaries to pay for scholarships - which is kind of what we are specifically talking about here. I dont know a situation where a coach would really have to tell anyone he is covering fees, unless he wants it to be known.