Before I get to how the stream deck device might useful...
The reason this is useful is a have several name patterns I use and I don't want to have to re-type them over and over
It sounds like you may not yet be familiar with Snapshots. If you type your rename string the way you want it, and then click the lightning bolt, you can save that rename string and it will always be accessible from that lightning bolt menu.
You could also rename your images on Ingest with the appropriate string, delete the bad ones, and then essentially just have Photo Mechanic re-number the remaining images, without having to type the string that you used on Ingest (which you can also load from a snapshot of the Ingest window). If you're interested in that I'd be happy to talk about how to set that up.
Now with regard to the Deck. I've never used this device, but I watched their intro video and I can see how it could be useful. When you open the rename window, the text in the field is highlighted. So set a shortcut to Command+M, and then set one of the other shortcuts to paste the relevant text. Make sure that text is followed up by the Sequence Variable and you should be good to go. Map another key to the Return key and in 3 keyboards presses your images are renamed. I didn't see if this was possible but if you can program one button to multiple shortcuts in sequence, then that could cut that down to 1 button press, but that might be tricky, because if you have a large number images selected for renaming, it may need to gather their metadata for a moment before it brings up the Rename window.
Let us know how it goes.