Is a relational database with a dynamic number of tables a good design?
Is this a bad design?

Yes.  See comment by LowlyDBA.

Is there a limit to the number of tables in a database in RDBMS ...

Each RDBMS has a different maximum number of tables.  There is a Q&amp;A for this is on Stack Overflow.

Should I use any different datastore to achieve this other than RDBMS?

No. RDBMS should be fine if you design your schema correctly.

Any suggestions?

From your description, a single table with Entity_Name as part of the Primary Key should work. A table with 100M rows is not a problem for today's databases.
create table data_for_entity (
  entity_name     varchar(50),
  entity_id       int,
  entity_value    text, -- or whatever PostgreSQL uses for JSON
  constraint data_for_entity_pk Primary Key (entity_name, entity_id)
);