Hello @Lucie_Pospechova,
Welcome to the community.
First of all 
for explaining things in detail.
This is a direct solution for you.
Formula: REGEX_MATCH({Image field},"Stored Image name in Airtable without extension")
To remove file extension from the name you need to use Make’s string functions.
If you need to understand it more.
Understand the Basics
You need to understand things about how the Airtable formula function works here while you use it with API or in make 
I’ve also explained on the attached screenshot but you can check more here.
There are lots of Airtable community posts about it. Search and read it.
I hope this helps you.
P.S.: Always search first, Check Make Academy. If this is helpful, Mark Best as Solutions 
and give
If you need expert help or have questions? Contact or comment below! 