Very typical and very annoying situation unfortunately.
WordPress doesn’t “pull” update information. Instead it submits plugin and theme information to the API at wordpress.org, which responds with updates available. In practice matching of updates is loose and exact logic is not disclosed. Name matters a lot, folder name as well. Rest matters to some unknown degree.
The closest to solution is filtering your theme’s data out of HTTP requests to the API via http_request_args filter. There is old post on topic excluding your plugin or theme from update checks, but as of recently API requests had been changed to use JSON and code no longer applies as-is.