Yeah, it basically doesn't mean anything unless you want it to. I don't think any of my characters actually worship the deity I assigned them as guardian. In gameplay terms, the main thing it affects is whose symbol appears on your side of the chapel if you ever get a Ceremony of Eternal Bonding done.
It's not like a birth stone, though - there are already month assignments for the deities based on your character's nameday month (not their guardian deity):
January (1st Astral Moon) - Halone
February (1st Umbral Moon) - Menphina
March (2nd Astral) - Thaliak
April (2nd Umbral) - Nymeia
May (3rd Astral) - Llymlaen
June (3rd Umbral) - Oschon
July (4th Astral) - Byregot
August (4th Umbral) - Rhalgr
September (5th Astral) - Azeyma
October (5th Umbral) - Nald'thal
November (6th Astral) - Nophica
December (6th Umbral) - Althyk
You'll hear NPCs refer to this on rare occasions - for example, during the 2016 Valentione's event, an NPC referred to Aghural as having been born under Althyk's watch, because his DOB is in December. His guardian deity is Byregot.
It's not like a birth stone, though - there are already month assignments for the deities based on your character's nameday month (not their guardian deity):
January (1st Astral Moon) - Halone
February (1st Umbral Moon) - Menphina
March (2nd Astral) - Thaliak
April (2nd Umbral) - Nymeia
May (3rd Astral) - Llymlaen
June (3rd Umbral) - Oschon
July (4th Astral) - Byregot
August (4th Umbral) - Rhalgr
September (5th Astral) - Azeyma
October (5th Umbral) - Nald'thal
November (6th Astral) - Nophica
December (6th Umbral) - Althyk
You'll hear NPCs refer to this on rare occasions - for example, during the 2016 Valentione's event, an NPC referred to Aghural as having been born under Althyk's watch, because his DOB is in December. His guardian deity is Byregot.