Logistics of a third, made-up last name

My husband and I have different last names. Let's say Buzby and Plotz. We're finalizing our top baby names and are heavily considering making up a third last name for our baby that is a combination of our names - e.g. Plotzby.

We don't want to hyphenate because my sister and SIL both had hyphenated last names and found them annoying to deal with (for example, can't be accommodated on forms).

My main concern is the day to day of dealing with a third last name for your child. If anyone has done this or something similar, do you have trouble flying or signing up for school or anything similar. I'm thinking that a similar concept has to happen with some frequency (like a parent who got remarried who has kids with their old last name) but still curious about the logistics.

Edit: I also couldn't see some of the flair options so had to pick postpartum recovery even though I think this is advice or discussion.