Yes, any user can change the Plymouth theme by placing their preferred theme in the directory
/usr/share/plymouth/themes
Making your own custom theme is more involved than a post will cover, so for now, let's try searching for an appealing theme you like.
I prefer the Zorin OS 15 splash (The following is a download link):
https://launchpad.net/~zorinos/+archive/ubuntu/stable/+files/plymouth-theme-zorin-logo_2.2_all.deb
Running the above .deb will install the theme, so all you would need to do is go about applying it using the steps below under Application of Theme.
If you prefer a different user made custom theme, you can search for them here:
For those not downloaded as a .deb self-installer, you must extract the file contents to /usr/share/plymouth/themes, then open a terminal to apply the theme.
Application of theme
sudo update-alternatives --install
/usr/share/plymouth/themes/default.plymouth default.plymouth
In the below, change EXAMPLE with the actual theme name as it appears in the directory you moved:
/usr/share/plymouth/themes/EXAMPLE/EXAMPLE.plymouth 100
Choose the theme you wish to use:
sudo update-alternatives --config default.plymouth
Look for the theme name from above listed in the numbered list and look at the corresponding number. Let's say that the new theme you installed is listed as number 2
Then you will enter in 2 in the terminal after the line asking you to enter the selection number.
Once done, you must update the system configuration so that the changes you made take effect:
sudo update-initramfs -u
Reboot and test...