I'm a known sperm donor, meaning I've donated sperm to a few women to help them have children, and I'm lucky enough to get a chance to visit and play with some of the children I donated for. Most of these kids know me either as Godfather or Uncle. In every case I've agreed not to try to take on the parental role. As much as I like visiting and spending time with the kids I feel it's better to allow the mother and her spouse, when relevant, to be the parents in charge of making decisions rather then confusing the child with two different sets of rules and parental expectations. Most of the kids know I donated sperm for them (not all of them fully understand what that means), but some are unaware and just know me as that fun guy that comes over to play. The kids are preschool age or younger, but one or two of them have older siblings I didn't donate sperm for who are welcome to join in with our games.
I've had a number of cases where the kids end up calling me Daddy, or some variant of that. it's never been because they knew I was a donor, instead it was because they had generalized the term 'Daddy' to all men, or they thought it was funny, or most often because they wanted to play 'family' and as an older male they naturally wanted to assign me the role of father in their game.
Most parents don't mind this, especially if I speak with them about it before or afterwards, but some aren't entirely comfortable with the kid's referring to their sperm donor as daddy, no matter the situation. I know one mother had a bit of a shock when her toddler first started calling me Daddy during my first real long visit with her (the child already called the man who ran her daycare daddy since all the kids had picked it up from the man's children, The mother presumes the child just generalized it to use for all men that play with her). I didn't get invited back for a little while after that, because, despite the mother fully understanding the reason, that it meant nothing to the child, and that I had not encouraged it, she still didn't know how to respond to the experience of hearing her daughter call me daddy. I eventually did get invited back and that girl is now the child I see second most of all kids and by the age of four she could, and did, explain in extensive detail the entire donor relationship, including explaining about sperm and 'tiny eggs'. While in that case we did recover from the early 'hiccup' of the child calling me daddy I'd still prefer to avoid moments like this whenever possible.
Generally I've spoken to the parents of the kids I'm allowed to visit and this isn't a big problem, but I'd still prefer to avoid kids calling me daddy in case of upset feelings from the parent(s) over the term. However, I don't want to make such a big focus on trying to avoid the term as to upset or confuse the children, or to make them ask why 'daddy' is a problem term, especially if they don't know I donated for them yet. For the kids that do know I donated for them I don't want to imply there is something shameful about the donor relationship or so wrong about it that it's wrong for them to call me daddy.
So what can I do to minimize kids trying to call me Daddy without being so blatant in avoiding the term that I do more harm then good.
I have, in the past, asked to be 'mommy' when playing house instead of daddy. I figure this avoids the dangerous D word while also opening them up to the concept of trans and non gender-binary individuals in a small way; generally after a moment of confusion kids don't have an issue humoring the request. However, I sometimes get "You can't be Mommy because I want to be Mommy" response, and while I have pointed out that a baby could have two mommies I can't always justify going through that much effort every time kids want to play a simple game, they get frustrated when you argue over what they see as semantics every time. So while it has proven an option at times it's not a single foolproof option.