If we follow the etymological path of anniversary:
from annus (genitive anni) "year" (see annual (adj.)) + versus, past participle of vertere "to turn" (see versus).
we can come up with dieiversary as a neologism. (or it can be simplified as diversary or dieversary). Though diversary can be confused as a form of diverse. (or a second anniversary?). I can see that some people already thought about this when you do a search.
In Latin, diēs is day and the genitive form is diēī.
Note: There is also a neologism diaversary which is used for the diabetes diagnosis anniversary.
On the other hand, we would call it a curious coincidence in a normal day. What a coincidence that Merriam-Webster has this example usage:
By a curious coincidence, they bought a house the same day their old one burned down.
Though there is a mathematical and astronomical explanation for the reason that an anniversary can fall on the same day of the week. Usually the first anniversary wouldn't fall on the same day of the event, unless a leap year day occurs on the first year of the event. Because 365 has a remainder 1 when divided by 7 and adding one day gives you the next day of the original event day.
You might say coinciding anniversaries also but it is usually used when the anniversaries of two different events coincide. Though it can be applied to the coinciding anniversaries of the same event.