It would be great if we could see some communication from your Deity from time to time, like in a special dungeon or harder place. You could get a hint at what you might need in terms of spells that is offered from your Domain choices if suitable choices are available, or just in general from your spell list. Just something to make the player feel they're actually playing a Cleric, or Paladin etc. You won't just be acting like a Cleric, you'd be feeling like one.
Doesn't have to be often at all, just some locations where you get to feel like your Deity is indeed aware of you and your service and is looking out for you. This doesn't only have to be Clerics either, just about any class that have some sort of patron would do.
Just a few events like this would create the illusion that no matter where you are, you're not alone. Even though nothing is happening right there, no communication, the fact that you have had it at all would make you feel like it could happen at any time.
A GM could do this for you if you're playing PnP, but I can't think of a game that ever made me feel that way.
In 5e you don't have to chose domain spells, each domain spell is automatically known when you are of high enough level, and counts as a cleric spell.
If Larian puts the spells Commune and Augury in the game you will have your wish. Paladins, Clerics, and those with Ritual Caster: Cleric, Divine Soul Sorcerers, Tome Warlocks, and Bards that use their magic secrets feature can all have access to Commune and Augury.
Plus the cantrip Guidance.
Plus Clerics and Paladins have a feature called Channel Divinity, which is not a spell, but the ability to directly channel their Gods divinity through themselves to create effects. And Clerics have a special feature called Divine Intervention where the God directly intervenes, creating a miracle, usually via cleric spell of any level. You roll to see if it happens unless you are level 20 then it automatically suceeds.
Plus there is the Acolyte Background.
XGTE has cleric a spell called Temple of the Gods where you sumon a magical Temple dedicated to your God and another cleric/paladin spell called Ceremony which has the ritual tag, and has a variety of choices of magical/religious effects, like marriage, dedication, atonement, make holy water, ect... Plus Hollow makes an area sacred to your God.
You know if you have Bane, Bhaal, or Myrkul as your God, if you meet them, they will likely treat you differently, in fact I'm betting you will be able to side with them.
There are three main Temples in BG, so it's also likely if you worship that God you will get extra dialog options, especially if you area cleric. The Planar Ally spell will usually provide you will a servant of your Gods as an Ally, although techniquely you can request an Ally of any Cosmic Being, Primordials, Archfiends, Archcelestials, Archfey, Dark Lords, the Raven Queen, other Gods then your own, ect...