I attached some images, as they would be able to image my explanations.
One software seems to be using a font size that matches thee note with it's associated b or # all within the size of a piano key of the virtual keyboard shown.
(the software with the white bar on top), and seems to play with font size when it is needed to accommodate such demand.
whilst the other software, when it comes to close notes such as your C and C# example, seems to shift to stack the notes names one after the other without regards to them being right on top of the notes.
I must say though, that both these softwares have an option to choose the scale in which we want the notes to be displayed in when keys pressed, so to have notes named C then Dd (if set for a Db scale for instance...) rather than C then C# then D D#...
which is wayyy better to have btw, specially for us giving video tutorials. But I do understand that it would add on the coding complexity. I apologise in advance. At the same time it only increases the portability and usability of your software.
To be honest, the notes on top of the bar would be way more appreciated than the current mode (for esthetics purposes) and also which the current version lacks the names of the notes for the black keys (which is really helpful for piano very beginners receiving tutorials).