Since Cassandra 3.4 (3.5 recommended), LIKE queries can be achieved using a SSTable Attached Secondary Index (SASI).
For example:
CREATE TABLE cycling.cyclist_name (
id UUID PRIMARY KEY,
lastname text,
firstname text
);
Creating the SASI as follows:
CREATE CUSTOM INDEX fn_prefix ON cyclist_name (firstname)
USING 'org.apache.cassandra.index.sasi.SASIIndex';
Then a prefix LIKE query is working:
SELECT * FROM cyclist_name WHERE firstname LIKE 'M%';
SELECT * FROM cyclist_name WHERE firstname LIKE 'Mic%';
These examples and more configuration options, like suffix queries, can be found in the documentation
A more in depth explanation about how SASI works can be found here.