Dear Adobe / Kyle. Please consider!...

It's quite easy to rename them at once by scripting. You simply remove 'Kyle's Inkbox ' from each name running the script in up to few secs for thousand presets I guess. When you're decided for such move, move your topic to Photoshop Scripting

There're some examplary codes that alert you of clicked Brush Preset name, but may be modified or completely rewritten to loop over all presets and simply rename common part to empty space: Getting the name of the current brush preset

Edit1: I checked my 1st script and it works wrongly in CC2018, not like used in earlier versions. But 2nd one with no change.

Edit2: what a shame, I just found my other script that detects renamed Brush Presets and it works bad in newst CC2018

Okey, this is FINAL EDIT / here's your script:

function sTT(v) {return stringIDToTypeID(v)}

(ref = new ActionReference()).putEnumerated(sTT('application'), sTT('ordinal'), sTT('target'))
lst = executeActionGet(ref).getList(sTT('presetManager')).getObjectValue(0).getList(sTT('name')) 

for (i = 0; i < lst.count; i++) {
     if ((reg = /Kyle's Inkbox - /).test(nme = lst.getString(i))) {
          (ref1 = new ActionReference()).putName(sTT('brush'), nme);
          (dsc1 = new ActionDescriptor()).putReference(sTT('null'), ref1)
          dsc1.putString(sTT('to'), 'Ink-' + nme.replace(reg, ''))
          executeAction(sTT('rename'), dsc1, DialogModes.NO)
     }
}

Copy it, open Notepad, save as "Inks.jsx" (note you have to replace *.txt in Fiie's name field to that exact name, including double quotes!) Put this script at end of: C:\Program Files\Adobe\Adobe Photoshop CC 2018\Presets\Scripts (it may be little different for you). Reopen Photoshop (if launched). Finally you should find your script in File / Scripts. After you click Inks, and open Brushes Panel, you will see changed names.

Let me know if it doesn't work though I tested it, or you want it to be somehow modified. Btw I forgot in last post to attach link to other script that detects renamed Brush Prestes (however it works in earlier Ps versions): Re: Brush Rename Event

Not exactly the solution you are seeking but it may help a little.  You can change your UI Font Size to Tiny so you can see more of the brush names.  Go to preferences > Interface > Presentation> UI Font Size > Select Tiny.  You will need to restart photoshop.