I recently found some more info about St Gertrude which makes the connection with Hamlet's Gertrude even tighter than I'd previously realized:

St Gertrude of Nivelles is the patron saint of gardners . . . . mentally ill people (especially those with a rat phobia), travellers, pilgrims . . . , recently dead people, and graves. . . She's associated with mice, which represent souls in purgatory. - extracted from the following link:
"Praying to Saints and Folk Magic: Santa Gertrude di Nivelles (2010 Myth Woodling)"
http://www.jesterbear.com/Aradia/SantaGertrude.html

St Gertrude of Nivelles is the patron saint of gardners:

HAMLET (1.2.137)

...'tis an unweeded garden
That grows to seed; things rank and gross in nature
Possess it merely.

HAMLET [speaking to Gertrude] (3.4.167-168)

. . . do not spread the compost on the weeds,
To make them ranker.

St Gertrude of Nivelles is also the patron saint of mentally ill people, especially those with a rat phobia:

HAMLET (3.4.27)

How now! a rat? Dead, for a ducat, dead!

CLAUDIUS (3.2.232-233)

What do you call the play?

HAMLET

The Mouse-trap.

"Gertrude of Nivelles' symbol, the mouse, is said related to the souls in purgatory."

FRANCISCO (1.1.11)

Not a mouse stirring.

GHOST (1.5.13-17)

I am thy father's spirit,
Doom'd for a certain term to walk the night,
And for the day confined to fast in fires,
Till the foul crimes done in my days of nature
Are burnt and purged away.

St Gertrude's Feast Day is March 17, the same as St Patrick's, who is also a keeper of purgatory.

HORATIO (1.5.148-149)

There's no offence, my lord.

HAMLET

Yes, by Saint Patrick, but there is, Horatio, And much offence too.<

St Gertrude of Nivelles is also the patron saint of "travellers, pilgrims . . . , recently dead people, graves."

After Hamlet had been driven mad by listening to the the Ghost's forbidden tale of the secret's of his prison-house, Hamlet appears before Ophelia with "no hat upon his head" (2,1,87). Later Hamlet speaks of "The undiscover'd country from whose bourn no traveller returns"(3,1,87).Still later Ophelia sings of Hamlet with a cockle hat (4.5.28) Pilgrims wore cockleshells on their hats. Ophelia's song foreshadows Hamlet's "pilgrimage" to the "undiscover'd country" of her "chaste treasure" in the "womb of earth" (her grave). With Gertrude standing by, Hamlet returns from that undiscovered country with his sanity restored.
(See The Rebirth of Hamlet - http://www.thyorisons.com/#Rebirth)
.
Now aren't all you Freudian perverts ashamed of your spurious accusations against this saintly woman?