The proper way to join two beams on a post

If you pair the beams up, you should glue them with construction adhesive. Just nailing or screwing them together won't really distribute the load across both beams. Although; you're probably not planning on hanging or resting anything on just one beam and expecting the other beam to help with the load anyway.

A pair of 2x8 beams are going to be 3" wide (typically 1/4" is planed off each side of dimensioned lumber to give it the finished surface).

A 4x8 beam is going to be 3-1/2" wide. The extra half inch is going to add some strength to the 4x8 beam.

The 4x8 might be more prone to warping than a couple of 2x8's if it's a solid beam (but not if it's a laminated beam).

If this was for indoor use, you could sandwich a strip of plywood between the 2x8 beams and glue (not nail) all three pieces together to create a laminated beam that would be stronger and less prone to warping than the 4x8. But since you're building a deck, the sandwiched plywood would soak up water and be a problem.

There are lots of ways to attach beams to posts, and you don't necessarily need purpose-built brackets. Miter your beams so that they come together at an appropriate bisection of the post top, and use whatever means is convenient to keep them positioned... dowels, angled screws, etc.

In the case shown in the second image, I'd be inclined to use a skewed hanger and hang the angled beam on the other two. If your beams actually have the offset shown, things are complicated a bit, but maybe a short third member bolted to the right-hand beam would flush things up in simple fashion.