Effects of the same name don't stack
Initially, Legendary Resistance was rather solely a monster-only trait, only acquirable by PCs through the relatively rare means of becoming a monster that has this property, eg. a vampire like your character. Because this trait wasn't presumably meant to be available through other sources, there's no special rules regarding it - it's just a normal monster trait as far as the mechanics are concerned.
However, Rise of Tiamat does include the artifact Dragon masks that each provide the PC wearing them with one use of Legendary Resistance per day (available for free in this online supplement). This makes it possible to have a Legendary Resistance from being a vampire and from having the mask, but this is a rare edge case without any specific rules attached.
Fortunately, Jeremy Crawford, the lead rules designer of DnD 5e, has resolved the situation with a tweet:
Effects from game features with the same name never stack.
Therefore, you're limited to using either the one use of Legendary Resistance provided by the mask or the three uses provided by your vampirism - already quite a powerful boon, so I believe this judgment is better for balance than allowing stacking.