I like to think of Shiny Pokémon as 'the specimen made just for you', since, if the two halves of a Pokémon's PID, your TID and your SID all XORed together equal less than 16 (indicating a very small deviation), it will be Shiny.
One thing I really liked doing SwSh was actually giving my Pokemon a little personality to them. For example my, Dottler, Radar. Radar in camp always wanted to race someone even though he'd lose because he's a Dottler. He also really enjoyed chasing after the ball. This gave me the idea that he had a bit of an underdog complex and thrived off the losses to grow stronger. In game, he loses by the same amount each time. In my head, he got just that bit faster. This even worked for battles because Radar...wasn't the most effective member of the team. This all led up to his evolution into Orbeetle where its speed could finally rival the rest of my team. Still....not the best in battle but I loved him too much to care. While SwSh weren't my favorite games, I will say I felt pretty attached to the team I made.
One idea I’ve always had to personalize Pokémon was if every Pokémon had an unique idle/battle animation to match their nature to give them more personality
The MCs in the Adventures manga have naming schemes (unless they’re Silver or Blue) that’s usually a syllable from their Pokémon’s name with a suffix. For example, Gold’s scheme in the Japanese version is (syllable)taro. His Togekiss is Togetaro, his Typhlosion is Baktaro, etc. In English it’s just replaced with “bo” instead of “taro” and the English version of those syllables from their names. Sun has a cool one where all his Pokémon are named after currencies because the bread comes first.
Most of these titles come from ribbons, and most of these ribbons come from older titles. The Living Legend is only available from HGSS and would show everyone that you’ve had it since Gen 4.