As far as I understand it: technically yes, generally no. You can rename morphs, but anything that uses the morphs will break.
First, an alternative to consider is to change how the morphs are grouped in the parameters pane. If putting them in their own submenu would help keep track,
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. (There used to be
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to help you do this in bulk, but it seems to be gone now.)
If you really want to rename morphs: if you're talking about morphs from a standalone morph pack, you could rename those, since normally nothing else built-in is using them. But anything that
is using them--like your existing scenes and characters--would break! Similarly, you can't rename the morphs built into characters and clothing, since those would break. (Daz references the morphs internally by name, and so if you change the name, it can no longer find the matching morph.)
If you still want to rename them, I don't know if there's a way to do it internally to Daz Studio, the only way I know is: (1) use the batch converter (it's a pane in Windows -> Panes) to uncompress the .dsf file corresponding to the morph; open the .dsf file in a text editor and replace the old name with the new name in around 5 different places (multiple fields like "id", "name", "label", and "url").
(It may be possible to change the displayed name w/o changing the internal reference name, It didn't seem possible in my quick testing, but there are a lot of combinations of the 5 fields to change or not change.)