Each system needs a way to tell whether a new enquiry is a new person or someone it already knows. Most use the email address. HubSpot, for example, needs an email address on a form by default before it creates a contact.
Without an email address, matching gets less reliable. HubSpot has a setting that lets forms without email create contacts, using browser cookies to match visitors. It warns that two people sharing a device may end up linked to the same contact.
The simple fix is to ask for an email address on every form and booking. Keep the field names the same across systems. For example, use separate first name and last name boxes everywhere, rather than one full name box in one place and two boxes in another.