How to input unicode symbols with search?

Often times, I use unicode symbols (emoji, blocks, arrows, math...) in my typing, but it's very annoying to search-copy-paste them from the interweb, and it's also quite tedious to customize the Compose key (ensure clash are not used, find a mnemonic, edit config, restart). So, I'm looking for a way to quicky insert unicode symbols by searching while typing. Is there a way to do that? For example, say that I want to write 𝛼 = 𝛼 + 1. I would like to press a magic key (like Compose), write "alfa" or "alpha" down and get the suggestion for 𝛼 and 𝛢 (capital 𝛼), and maybe even other symbols related by relevance. This means that, in any application I am using, some kind of popup window should appear and help me search the right symbol. I recall of having seen something similar in the past for people writing in japanese or chinese, but I don't know what could work for unicode. What could I use to quickly search unicode entry points and insert them in the text I'm writing?