What kind of relationship would prefer to have with your pokemon? Do you prefer to be very close and affectionate? Professional working level only? Distant? For example some pokemon may have that need to call the higher up a master. For example Lucario might. Or canine pokemon might even call the trainer “alpha”. Just my own musings.

I suppose the simple answer would be that I’d aim at least initially for a degree of professionalism – trainers always have expectations of their Pokémon, so it’s only reasonable that the Pokémon should be able to expect certain courtesies, services and assistance in return – with the caveat that any professional relationship is smoother if it’s also friendly.  I think my answer to this question has a lot that would interest you.

Now, as for what Pokémon “call” their trainers – bearing in mind that we don’t actually understand how they communicate, since they just don’t have enough phonemes for all the concepts they obviously understand, that’s tricky.  For a variety of reasons, I don’t believe Pokémon understand or have any use for the concept of personal names, so actually I think all Pokémon likely refer to their trainers as something like “human,” “master,” or “friend” (and yes, I know about the episode with the subtitles, and I know Pikachu has a specific sound for Ash – translation is a bit more complicated than that, even when going between two human languages).  You do raise an interesting point, though – different species will have different needs in this relationship and will react differently to trainers – even the anime tends to put this down to variations in individual personality, as do the fans, but differences in the psychology of entire species must be important too.  Lucario, I think, are supposed to be solitary by nature – a highly social Pokémon like Mightyena, famed for teamwork, will almost certainly need a great deal more micromanagement in training and more interaction with other Pokémon to maintain a balanced emotional state, while a Lucario might be happy being left to meditate for hours on end.  To take an extreme example, Kangaskhan, a Pokémon evolved for a very high degree of investment in her young, might come to view a (comparatively) small and frail human as a family member in need of maternal protection, and consequently be uncomfortable letting her trainer out of her sight for an extended period.  And then there are Pokémon that are just plain inscrutable, like Starmie or Sigilyph – even a very skilled trainer might have trouble figuring out what kind of relationship makes them happy.