From having a quick play on my system, I only have PCmanFM-qt and Dolphin installed on my Ubuntu Studio laptop. Right-clicking on a .WAV in PCmanFM-qt and selecting properties does not show any tagging information.
See screenshot below;
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However, right-clicking on a .WAV in Dolphin (KDE's default file-manager), I can see it does support tags in WAV files. There is an option to add tags in the main right click menu AND in the details tab of the properties page.
See the following screenshots:
Right click menu in Dolphin:
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Details tab of property page in Dolphin:
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NOTE: In the Dolphin images above, the icons for the .wav files aren't there, only the file-names. That's because I'm using dwm as my main WM and it doesn't play properly with Dolphin on KDE5. There is a workaround to fix that issue, but I haven't got around to fixing that yet. I only installed Ubuntu Studio on my laptop last week and haven't finished setting up my preferred dwm environment yet.
But everthing works properly in the Ubu Stu's default KDE/Plasma X11 session.
If your distros file manager doesn't allow you to change the properties of .WAVs to add metadata, you could perhaps try installing Dolphin, or switch to using a KDE/Plasma desktop session. Without looking at other desktop environments, IDK which other file managers have a similar ability. Also, I'm not sure if the WAV tagging capability of Dolphin is a default behaviour or if it's been added by a plugin/extension. I've only just switched to Ubu-Stu from Debian and I've been using dwm and pcmanfm for years, so IDK what's in a stock install of Dolphin in KDE/Plasma
Otherwise, if you don't want to change your Desktop or your file browser, then perhaps you could try using an application like Kid3, a QT based desktop application which allows you to add tags to audio files. I've never actually tried tagging .WAV files in Kid3, but from a quick look, it only appears to support ID3v2 tags in .WAV files.
Screenshot of kid3 below.
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Kid3 is pretty nifty. You open it to a directory containing music files. Then you can select multiple files and then set the tags that are common to all of the selected files in one go, like the Artist, Album, Year and Genre . Then you can individually select files and edit the more song-specific tags like the song Title and Track number tags.
Once you've added your tags, you simply select save in the main menu and all of the files in the directory will have the tags embedded in them.
Final notes:
.WAV is quite an old format. Tags aren't commonly used in .WAV files.
.WAV files can hold meta data, but it only supports very limited tags. It can hold ID3v2 tags, but most applications that process .WAV do not recognise embedded ID3 tags in .WAV because again, they're not commonly used.
Formats like MP3, OGG, MP4 (or M4a) and .WMA are better suited to tagged metadata, but they are lossey files. Or if you want something lossless like WAV, then FLAC or AIFF are better. Of the two, FLAC supports more types of metadata, is compressed (in a lossless way) and is open-source, whereas AIFF is a proprietary Apple format and is uncompressed and typically has larger file-sizes.