My Spanish girlfriend has an ñ in her last name, and as does our son. To the people here in Norway, I just tell them to put a plain n when typing the last name. It’s easier to just go with that than to try and get people to understand how to type ñ on the keyboard (even though our computers can do it), and to avoid extra back and forth with people who have systems that don’t handle it.
Likewise, when I’m in Spain I don’t bother to say that my last name has ø in it. I don’t even bother to rewrite the o in my last name as oe. I just put it as o.
The only situation where I put it as oe is indirectly when an airline converts ø to oe on my airline ticket, or where the airline system doesn’t handle ø and I put it as oe for them when making the booking. To me my name looks worse with oe in it, and seems harder to pronounce for people if I write it as having oe in it than just putting it as o.
My point was that someone who can type it will often have it rejected by a website. I was using a hotel booking site and when I booked a room it asked me for my address so I typed Å... The web page rendered it correctly but when I hit the button to complete the transaction it told me that my address contained an illegal character (or some similar wording). And this site handles bookings for hotels that themselves have names with umlauts, tildes, cedillas, etc.