#1: Don't reveal your villains' names.

The spell states (emphasis mine):

When you cast this spell, you can speak the name of a specific creature (a pseudonym, title, or nickname doesn't work).

A villain who is aware of the Gate spell would not tell his name to others. Hence, your players cannot summon him, if they only know him as "evil wizard of the east" or "the hero of Parnast" (yes, that guy is a villain, no further discussion necessary).

#2: Use Contingency with Otiluke's Resilient Sphere.

You can also cast the Contingency spell on yourself, using "when someone other than me teleports me" as a trigger, and make the spell trigger an Otiluke's Resilient Sphere.

Note that this sphere can be dispelled or destroyed with Disintegrate, so it won't work if your PCs anticipate the use of this sphere.

#3 Have an active Clone residing in an area protected against teleportation and planar travel.

The clone spell allows you to grow an "inert duplicate" of yourself. If / once you die, your soul transfer to this clone, allowing you to "respawn".

If you put your clone on a Demiplane affected by a permanent Forbiddance spell (i.e. you have to cast the spell there 30 days in a row), then you can't be immediately resummoned and killed permanently, either. You don't technically have to put your clone on a Demiplane, but since it's a lot harder to travel to a demiplane and kill your clone than it is to travel to a remote castle on the material plane, I highly recommend using a Demiplane.

Note that Forbiddance may prevent you from traveling to your Demiplane. If you leave a small part of your Demiplane unaffected by Forbiddance, it shouldn't be an issue, though.