Why do some R. Digbyana have names? ex. 'Alpha'
 

I've seen sellers mentioning specific names for their R. Digbyana, like "Mrs. Chase", and "Alpha". I can see in pictures that they look slightly different, but why are certain Digbyana well known and named?

The name following a species or hybrid name inside a single quotation mark is a clonal name.
Unless a plant is a mericlone, each seed propagated plant is a unique individual and may carry different features that set them apart from others within the same group, although this difference may not be very significant, especially for a species or a primary hybrid.

Mrs. Chase is a well known clone of R. digbyana for its especially nice form among the crop, and I believe has been awarded also.

I hope this helped in any way.

I just want to add that the named clones are generally awarded by the American Orchid Society. You get to name your plant if awarded.

This is not entirely correct. Anyone can assign clonal names to their plants. However, clonal names are not recognized or registered by anyone, unless the plant earns an AOS award (either quality or horticultural).

Most breeders have multiple plants on their stud bench, each of which has some desirable trait (shape, size, color, vigor, length of inflorescence, number of flowers, etc. etc.). To distinguish these from each other, it is common to assign a different clonal name to each.
Many of these will never earn an AOS award, as the overall quality is not sufficient. Yet, plants which pass their desirable traits to the offspring are valuable in their own right, and other breeders will seek out divisions.

How would one go about growing a plant to be awarded and name it?

Grow the plant from seed? Bloom it, have it judged, and win.

Are the awarded digbyana that sellers like Odoms sells all divisions of original plants? Have those plants been grown from seed, and then some been mericloned, like Mrs. Chase, to be mass produced as opposed to just selling by division?

I find the whole process very interesting. Sadly I haven't been able to join my local AOS yet because their meetings conflict with my work schedule.

Any plant can be submitted for AOS judging, which takes place:
A. Once a month at the regional judging center.
B. At most of the orchid shows sponsored by local orchid societies.

I have received 8 awards over the past 10-12 years. Most were seed grown plants, but at least one was a meristem, which had an exceptionally good blooming that year.

Most of the plants offered for general sale are either seed grown, or meristems. The seller should know in each case.

On occasion you will find an original (non-meristem) division of the awarded plant. These are often called 'mother divisions', and are at an entirely different price level from meristems. Depending upon how recently the award was granted, and how many divisions are available of the plant, prices can be:
Cattleya: anywhere from $50 to $1,000 or more
Paphiopedilum: (which can't be meristem propagated), $150-3,500 (or even 5,000).

Yep, this is why I said "generally." The overwhelming majority of plants available on the market for general consumption with names have an award attached to them.

Grow a plant from any source: Seed, seedling, meristem, division. Flower it. Take it to an AOS judging event or judging center.

Exactly! Judging centers meet once per month and shows typically happen once per year. You can get your plants judged at both events.

South Florida has a ton of judging centers and shows, so finding a local judging event should be fairly easy! Folks at your local society will know more specifics.

Don't you have to have grown the plant for at least 6 months before taking it for judging?