I’m an animal behavior/veterinarian student (primarily with canids), so while certainly no expert, I can hopefully add a bit of animal-related knowledge.
As you and frostypuppy mentioned, I’m sure each Pokemon species’ intellectual capacity would factor in here. Pokemon that can fully understand the lexicon, symbols, and other nuances of human language I would think could be simply told that your name is representative of you.
Assuming the majority of Pokemon that aren’t that intelligent are capable of discerning motion, visual, and acoustic cues like dogs can would be more difficult to teach.
In short, when you begin to teach a dog a new command, the vocal direction you choose in a vacuum is irrelevant. “Come,” “Stay,” etc. are very intuitive for humans (including for individuals that aren’t teaching the command) and as such are often used as they are meaningful to us. The dog will eventually assign meaning to these words, but not before associating something relevant to them with it.
As such, associating you with a name needs to be tied to something that has meaning to the dog or Pokemon. Dogs are individuals, and are enticed by different things. Just like Pokemon that have characteristics (e.g., likes to run, etc.), treats are often effective but some dogs associate more value through attention, or are selective with what treats are worth obeying for.
So before attempting to assign meaning to your name, you may need to have an ample supply of batteries for a Joltik, be ready to play many games of fetch with a rowdy growlithe, or lots of quality yarn for a litten. The point is that your enticement should be individualized.
Next, I’d assume your name needs to become a clicker of sorts. Clickers are often useful in training to help dogs make complex associations simpler. Before a dog can learn to stay, then come; it needs to know what “staying” is. Positive reinforcement is most effective, so a click immediately followed by your enticement of choice will over time make the “stay” command relevant.
In order for your Pokemon to associate you with your name, it needs to be incentivized to correlate your name to a meaningful event. As such, perhaps a possible approach would be to have the Pokemon learn what “come” means. Then, you and another trainer can each have your enticer, but the enticer is only given when your Pokemon comes to you. I.e., “Come to lyleberr” + ampharos comes to you = reward. “Come to lyleberr” + ampharos goes to the other person = no reward.
I felt like I’ve rambled for this Tedtalk long enough, haha. Hopefully that’s something remotely close to what you were looking for, and thanks to anyone who read through all of this 
