You don’t need to have it match your social link Arcana, that just gives you EXP bonus on fusion so the resulting Persona will end up with a few extra levels and skills beyond what it shows on the fusion screen.
You can’t fuse a Persona of a higher level than you, but if you have a social link ranked up of the same Arcana, you can end up with one of a higher level than you through the EXP bonus (it just has to start at a base level at or below your own).
You want to fuse your lower level Personas into higher level ones closer to your own level, with better skills. Just experiment with what you can fuse – anything you fuse away you can always buy back by summoning from the Compendium.
Any Persona you fuse or get through a card is automatically registered in the Compendium, however you’ll need to overwrite the registration when they level and gain new skills, they don’t automatically update. Which means if you get your Orpheus up to level 15 and fuse it away, but never re-registered it, if you try to summon it later, it’ll be all the way back at level 1.
Hope this helps! Just bear in mind that you’re not expected to keep any particular Persona for any real length of time, you want to be frequently fusing to make stronger Personas all the time. You’ll want to pay more attention to the skills you want to keep when you fuse than the Persona itself.