Is most important for organizing customers, right now someone text only first name or only last name, or someone text before last name and then first name or the other way around.

If I understand this request correctly I think it is asking for a separate filed for the customers last name.
If so I 100% agree.
I am getting a lot of bookings with people only putting in the first name.
I need both!
So I then have to waste everyone's time by emailing the customer for their second name.
We need a first and last name fields.

The work around linked above is not sufficient. This needs to be on by default. The last name is needed on the sign up page. aka under the "details" section when viewing Manage > Clients. it would also give us the option to sort by last name on the Manage > Client page.

To split the field into first name and surname is a must for me. And both fields need to sit on the main customer form applet as well as the form of address and title.
The solution mentioned in the description is a workaround but definitely not enough

This is available only for Client Login. I don't need that my client make account. This feature should be in Intake Form too

Above you say that feature exists. Not exactly accurate. That field can only be added if you activate "client login" which is an issue for us after importing csv file with email attached it creates an error when client is trying to open an account. The first issue I had was during import "first name" and "last name" were imported from excel as it appears on most data bases but yours is default "name" which causes error during import. Idiotic. Two fields for import and two fields for client booking.