I need to rename fk constraints (drop all fk, create new ones), but MySql (cuz InnoDB engine) created indexes for these constraints. Do I need to drop indexes manually? Or it will lead to issues? Please, somebody describe me this point.
It will not lead to issues.
Adding an FK should discover that there is already a sufficient index and not add a second one. Even if it adds a redundant index, little harm is done.
I wonder -- Why do you care what the constraint names are?
From 5.6 doc: "For ALTER TABLE, unlike CREATE TABLE, ADD FOREIGN KEY ignores index_name if given and uses an automatically generated foreign key name. As a workaround, include the CONSTRAINT clause to specify the foreign key name: ADD CONSTRAINT name FOREIGN KEY (....) .." and "Adding and dropping a foreign key in the same ALTER TABLE statement is supported for ALTER TABLE ... ALGORITHM=INPLACE but not for ALTER TABLE ... ALGORITHM=COPY."
My point in bringing that up is that ALTER usually runs faster if you throw all the changes to a table into a single statement. But DROP + ADD is disallowed in the COPY case.