'Found' creatures (familiars/steeds summoned with Find Familiar, Find Steed or Find Greater Steed) are a summoned spirit manifesting in different forms. For each spell, it is a single spirit that is summoned and re-summoned after any particular form drops to 0 hit points.
You gain the service of a familiar, a spirit that takes an animal form you choose. [...] When the familiar drops to 0 hit points, it disappears, leaving behind no physical form. It reappears after you cast this spell again.
You summon a spirit that assumes the form of an unusually intelligent, strong, and loyal steed. [...] When the steed drops to 0 hit points, it disappears, leaving behind no physical form. You can also dismiss your steed at any time as an action, causing it to disappear. In either case, casting this spell again summons the same steed, restored to its hit point maximum.
Find Greater Steed:
You summon a spirit that assumes the form of a loyal, majestic mount. [...] The mount disappears temporarily when it drops to 0 hit points or when you dismiss it as an action. Casting the spell again re-summons the bonded mount, with all its hit points restored and any conditions removed.
In each case, when one form is dismissed or killed, a familiar that is later summoned again is still the same spirit. In the absence of any reason to think they lose all memories and personality, it makes more sense to treat these as continuous.
Dev commentary, if dev interpretation is of interest:
A spell doesn't erase/suppress your memories unless the spell's text says it does.
When the text of a spell, like polymorph, says you retain your personality after a transformation, that's a terse way of saying, "You're still you, despite the radical changes you undergo." #DnD