Even before the telephone came to Tucson, directories of businesses and residents were published. This first image is from the 1901 directory, page 66. It shows that a person named F B French lived at 637 S 4th Avenue, my house. If you are scrolling through the PDF copy of the directory, it will show as page 89 because of the un-numbered pages which are counted by my PDF software. If you scroll through to page 109 of the pdf, you will find another name, O H J Johnson, associated with the same address. This is page 86 of the paper directory. Paper copies of the directories can be found at the historic society but they are in resident name order so finding a particular address is very difficult.
Here is a sample page of the 1901 directory. This link will let you see all pages of the directory: https://drive.google.com/file/d/1YdvSsdcHKxqezLKVnbAsTF6pG7OoPJmv/view?usp=sharing
Your browser or other software may allow you to search for and view the resident in 1901 of your property.