Is it possible to search Patternarium for a specifc preset by Name?

No, it's not. You can only find it if you know exactly what name and generation using the direct URL to the pattern.

You can get the generation lists if you dig around a bit using the list URLs. I can also help you look for it if you want.

Thank you Fredrik.
Using that link you gave, I found the one I was looking for in Gen=26. Nonuncitan Unperfectified.
And using the URL logic found it here: https://soniccharge.com/patternarium#/26/Nonuncitan-Unperfectified. Great!

So, I can see it can be tricky to locate, but glad for your help, that it is possible to do.