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Bear with me as the question is more specific than mentioned in the title (otherwise too long as a title).
Imagine this setup:
Site B contains a shortened url that links to my personal site (site A). If someone Google searches my full name, alidyn mcprono (example), will Site B ever appear in the search results? (ideally not)
Assume that there is no other reference in Site B of my name other then the shortened version ali.
Technically it should work as it's a 301.
About 8 years or so ago I did the same. However I would like to give you a heads up regarding URL shorteners - my ones all vanished when the company folded. Likewise another bunch stopped working when the url shortener changed their url structure.
I'm kinda glad I did not use too many of them as they'd all need to be changed.
Google will be able to find your site based on that link. When Googlebot crawls the site that links to you it will see the link to the URL shortener. Then Googlebot will crawl the shortened URL and see the redirect to your site. Googlebot will then crawl your site. Google will associate the anchor text of the link (the shortened form of your first name) with your site because of the link.
You might be able to find a URL shortener that uses robots.txt to block Googlebot. Then Googlebot wouldn't be able to determine where the shortened link is pointing. However, keeping your site secret is not a good way to keep your site out of the search engines. Google has many ways of discovering sites including monitoring domain name registrations. See Can a URL that is not linked to from anywhere be discovered? for a more complete list of ways that hidden URLs can be discovered by search engines.
If you don't want your site indexed in search engines, you should use a <meta name="robots" content="noindex"> tag in the <head> section of every page on your site. That explicitly tells search engines that you don't want anything to show up in search results.
You may see advice to use robots.txt to disallow crawling, however that is bad advice. Robots.txt does not prevent indexing. Google may choose to show a site in the search results even when it can't crawl it. See How to resolve Google “Indexed, though blocked by robots.txt” for an example. When your domain name contains the terms you don't want to show up for (your name), your site could end up in the search results for your name even if Google can't crawl your site. In addition, disallowing in robots.txt would prevent Googlebot from seeing the noindex meta tags. You want to allow crawling, but use the meta tags to prevent indexing.
