you need to define this when you create your Database and it depends on which database that you are using: here is a link that you can check out https://docs.mendix.com/refguide/case-sensitive-database-behavior
for example, if you are using sql server you still have the chance to change the collation and alter your database to use Case Insensitive, but there is a concern from Mendix that you will have more results from the DB retrieve action.
if changing that is not an option so the above solution by Joshua Choukroun is your way!
What you can do is to always store the project name in uppercase, then in your microflow you create a string variable like that toUpperCase($inputProjectObject/ProjectName), right after that you retrieve your object comparing this variable with the attribute ProjectName
You can try “contains” function in expression while comparing. contains function is not case sensitive.
hope this will help you.