How do I say whether or not a number was pronounced like a telephone number (or zip code). Are there words for this?

You are asking about "some proper terms".

In a comment, John Lawler said...

Most speakers have numbers (phone, social security, license, etc) memorized and their pronunciation will become ritualized in their speech. But we don't have a term for it.

But I disagree.

One of the terms might be the psychological concept ...

chunking

1. the process by which the mind divides large pieces of information into smaller units (chunks) that are easier to retain in short-term memory. As a result of this recoding, one item in memory (e.g., a keyword or key idea) can stand for multiple other items (e.g., a short list of associated points). The capacity of short-term memory is believed to be constant for the number of individual units it can store (see seven plus or minus two), but the units themselves can range from simple chunks (e.g., individual letters or numbers) to complex chunks (e.g., words or phrases). The exact number of chunks remembered depends on the size of each chunk or the subunits contained within each chunk.

APA Dictionary of Pschology

The chunking theory, developed by Chase and Simon (1973) was an important attempt to formalize the mechanisms linked to chunking. It postulated that attention is serial and short-term memory is limited to about seven items (Miller's magical number).

Springer Encyclopedia of the Sciences of Learning

This extends to long-term memorization and repetition of numbers in groups of three or more. The magic number seems to be 7.

There are different approaches to this process when repeating numbers such as telephone numbers, zip codes, social security numbers, etc depending on memorization and repetition. Quite often they are cultural.

That means that "double 00", or "oh-oh" can be considered as chunked, but the actual usage depends on the culture of the speaker.

It depends to an extent on the country in which you live. For example, in Greece (and, I believe, France) they recite in two-digit numbers, but with the word 'zero' ('Oh' or, in Greek, 'midhen' - as in 'me then') so for 1872 438962

eighteen, seventy two, forty three, eighty nine, sixty two

If there is an odd number of digits, different people do different things: some offer a single digit on its own and the rest in pairs, others pick a suitable three-digit number. This method works quite well in my experience.