Contact Other Plane says:
You mentally contact a demigod, the spirit of a long-dead sage, or some other mysterious entity from another plane.
Does the caster decide whom they are contacting? Do they have to name someone specific? Or is it random, or at the DM's discretion?
The spell doesn't really seem to care who chooses or how it's chosen.
If the caster was meant to choose (a specific entity) it would be worded to say something like:
You choose (or name) a demigod, the spirit of a long-dead sage, or some other mysterious entity to mentally contact.
Or
You mentally contact a demigod, the spirit of a long-dead sage, or some other mysterious entity from another plane, of your choosing.
If it was meant to be random it would be worded something like:
You mentally contact a random demigod, the spirit of a long-dead sage, or some other mysterious entity.
If it was meant to be up to the DM... Well you get the point.
As it is written I don't see that there's meant to be any one exact option so whether the players choose or the DM does, I'd say go with whatever makes the game more interesting and fun. Given that it's a 5th-level spell that can be cast as a ritual with a casting time of one minute (or eleven minutes) and only has the verbal component it's costing the party nothing but time (and maybe a spell slot) either way.
Trivially, everything is at the DM discretion.
Does it have a mechanical effect? Possibly ...
The DM answers each question with one word, such as “yes,” “no,” “maybe,” “never,” “irrelevant,” or “unclear” (if the entity doesn’t know the answer to the question).
If you were asking questions about a mysterious magical effect then a demigod of magic is probably going to know more than a sage who is expert in entomology.
How much of an impact depends on how much the DM (and the player's) want it to:
As an aside, crafting five questions with such limited answers that actually tell you anything useful is incredibly hard.
The spell as written doesn't specify the method of choosing.
That said, it's entirely possible for the DM to allow asking a specific individual. Likewise, it's entirely possible for the DM to pick based upon story, randomness, patronage, or even simply being a jerk...
It's important to note that the spell needs to be useful - otherwise, it's not going to get used. All spells in the game are intended to be useful. Therefore, if the DM is picking, and picks someone who wouldn't know the answers, the DM is then clearly not in line with the intended meaning of the spell.
So, that leaves us falling back to choices.
Since it only appears on Wizard and Warlock class lists, one can glean that that rules out the clerical patron (Cleric, Druid, Paladin). Well, not entirely - multiclassing is possible, and some campaigns allow characters to have a patron deity without being a clerical caster. If they have one, it is quite likely to invoke their patron or their patron's lieutenants.
The lack of a specified method is most likely to allow for tailoring to one's campaign world. My own home campaign, for example, lacks the usual panoply, being populated instead with humorous homebrew deities. If they'd specified, I'd have to rewrite it anyway.
In Adventurer's League play, I'm not going to specify whom, I'm just going to answer the questions in a nearly omniscient fashion.
If your player specifies who they ask, it's fine to get them that direct line. If not, pick by whatever means you choose. And realize that a failed save may be "dialed the wrong being" or "called at a bad time."
