Do I need a PTR for IPv6 as well?

Yes. If your server sends over IPv6, that address needs a PTR and an AAAA record.

Does the HELO name have to equal the PTR?

It should point to the same IP and ideally match the PTR. That makes the server look consistent.

Check reverse DNS (PTR) and HELO: set up your mail server correctly

Receiving servers look up the name for the sender's IP (reverse DNS) and check that this name points back to the same IP. If it is missing or looks generic, the spam score rises.

What is checked

The sending IP has a PTR record.
The PTR name resolves through an A or AAAA record to the same IP (forward-confirmed reverse DNS).
The HELO/EHLO name in the SMTP dialogue is a fully qualified hostname that belongs to the IP.
The PTR name looks like a dedicated mail server, such as mail.example.org.

Typical mistakes

The PTR carries the provider's automatic name such as 203-0-113-25.dyn.provider.net. Filters recognise such patterns as consumer IPs.
PTR and HELO name different hosts that do not fit the IP.
The A record for the PTR name is missing.

Where to set the PTR

The owner of the IP block maintains the PTR, which means your hosting provider or internet provider. You enter it in the customer area or ask support to do it. You create the matching A record in your own DNS zone.

dig -x 203.0.113.25 +short
dig A mail.example.org +short

Check reverse DNS (PTR) and HELO