We very often see the same username created across many instances

Guilty as charged. I’ll say though, there are several legitimate reasons why one might want to do this. I personally use it as a substitute for Reddit’s multireddit feature, by grouping community subscriptions across different instances by theme. As long as users use the same username across instances I don’t think this practice should be automatically regarded as an attempt to sockpuppet. It that was the goal, the accounts would definitely not be using the same username across all the instances.

When you search on a mastodon instance, some of the hits will be users. You can narrow down the search to show only those by explicitly specifying so. A segment of those users often look weird because they have no name at all and always share the standard lemmy default icon as profile picture. Like this:

Those are (usually) non-Lemmy Fediverse users, most of which are on Mastodon. You can click on them to see the profile and from that you should be able to follow them.

Edit: While it’s true that you can find Mastodon users on Lemmy using the method described here, you can’t actually subscribe directly to another user to get their posts in your feed, whether they’re on Lemmy or Mastodon. This notion of users directly following users is very much more in line with Mastodon’s design philosophy than Lemmy’s, so you’re probably right that you can follow a Lemmy instance from Mastodon but not the other way around. Please excuse my brain fart.

The only way I can see to make anything similar work would be to have hashtag bots like those described by @RxBrad@lemmings.world automatically post into relevant (or separate specialized) Lemmy communities, which admittedly seems like it might be interesting. Whether something like that already exists, though, I have no idea.