Running a case-insensitive cypher query

Another way would be:

WHERE LOWER(m.Name) = LOWER("Neo")

And if you are using the Neo4j Client (.NET):

Client.Cypher.Match("(m:Entity)")
    .Where("LOWER(m.Name) = LOWER({name})")
    .WithParam("name", inputName)
    .Return(m => m.As<Entity>())
    .Results
    .FirstOrDefault();

Yes, by using case insensitive regular expressions:

WHERE m.name =~ '(?i)neo'

https://neo4j.com/docs/cypher-manual/current/clauses/where/#case-insensitive-regular-expressions