implicit index created, do I need to also create an explicit index?

So I create a table with unique fields, and it creates an implicit index.

1. This is a general purpose index, correct? I.e. not used solely for
ensuring uniqueness, so I don't need to create another index on
the same field explicitly, right?

2. What are the implications of creating another index, such as
create index foo on tv_workspace(name)? Is is just a duplicate
of the implicitly created index?

create table tv_workspace (
name varchar(32) unique not null,
p4client varchar(64) unique not null,
owner bigint not null
);
NOTICE: CREATE TABLE / UNIQUE will create implicit index "tv_workspace_name_key" for table "tv_workspace"
NOTICE: CREATE TABLE / UNIQUE will create implicit index "tv_workspace_p4client_key" for table "tv_workspace"

TIA!
Mark

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Mark Harrison
Pixar Animation Studios