The gate spell says:

When you cast this spell, you can speak the name of a specific creature (a pseudonym, title, or nickname doesn't work). If that creature is on a plane other than the one you are on, the portal opens in the named creature's immediate vicinity and draws the creature through it to the nearest unoccupied space on your side of the portal. [...]

However, the size of the summoned portal is

5 to 20 feet in diameter.

What happens if you speak the name of a creature larger than 20 feet in diameter?

The rules are ambiguous

Here are two possible interpretations. Since there are two, you'll have to ask your GM whether this will work:

The creature is drawn through regardless of size

Spells do what they say, and no size limitation is placed on the "drawing through" effect of the spell. Whether or not the creature could fit through the gate normally, it is drawn through by this effect.

the portal opens in the named creature's immediate vicinity and draws the creature through it to the nearest unoccupied space on your side of the portal

If the spell could only draw through creatures that fit in a space equal in dimensions to the diameter of the portal, it would say so. Since it does not, this effect is not bound by the size of the creature.

Side-note: If you want a narrative explanation, most gargantuan creatures can squeeze through a space that huge creatures fit in (a condition that a 20 foot portal satisfies)

The creature can only be drawn through if it fits into the portal.

Since the spell specifies that the maximum portal size is:

20 feet in diameter.

Any creature that cannot fit will fail to be drawn through since you...

can't pull a creature through a hole that it doesn't fit through.

[credit to NautArch's answer]

Determining whether a creature can fit through the portal is an issue that NautArch's answer explores in a bit more detail. It's another question you will have to ask your GM as some creatures are too large to sensibly squeeze through a 20 foot hole (even though they are classified as gargantuan).

It's a bit up to the DM as dimensions may differ from size category

How does the Gate spell (PHB, 244) work?

The spell begins with a description of the size of the portal it opens (emphasis mine):

You conjure a portal linking an unoccupied space you can see within range to a precise location on a different plane of existence. The portal is a circular opening, which you can make 5 to 20 feet in diameter.

It then goes into what happens when you summon a creature whose name is known:

When you cast this spell, you can speak the name of a specific creature (a pseudonym, title, or nickname doesn't work). If that creature is on a plane other than the one you are on, the portal opens in the named creature's immediate vicinity and draws the creature through it to the nearest unoccupied space on your side of the portal.

While it doesn't specifically state that the size of the portal matters, it makes sense that the portal size is a limiting factor in what can go through it. You can't pull a creature through a hole that it doesn't fit through.

But that's where the Squeezing rules may come into play. The squeezing rules are explained very well and state that a Gargantuan creature (the largest size category) should be able to squeeze into the space when looking at the rules regarding creature size categories and the space they control. A Gargantuan can squeeze into a 15x15 space per those rules, but for creatures whose dimensions are listed, it isn't unreasonable to consider that with regard to the portal size.

We can look at the actual dimensions of the creature with regard to the portal size, and we'll use the Tarrasque as an example (MM, 286):

A scaly biped, the tarrasque is fifty feet tall and seventy feet long, weighing hundreds of tons.

That's a fairly big creature to fit into a 20' diameter hole.

While creature sizes are based more on areas of control, the rules on squeezing utilize those sizes. There does seem RAW support for both Yes(gargantuan size can squeeze through 20' spaces) and No(the listed overall dimensions are much larger and it doesn't make sense), and I'd leave it up to a DM as to how they adjudicate size descriptions vs size categories at their table to decide.