I read this book around 2011-2015.
The book had a little kid (unsure of gender sorry) who lived with some kind of older family member, not a parent, who was sent with provisions off to a magic school. Getting there required specific instructions and specific words/counting to get in.
The magic was plant based? Not as in growing plants, but something else. I think nettle was involved.
The cover was yellow and was also the name of some kind of plant.
It's a partial match, but might you be referring to Wizard's Hall by Jane Yolen?
The mother of shy Henry sends him to Wizard's Hall where he can train to become a wizard. At the Hall he is renamed Thornmallow, suggesting that he is prickly on the outside yet soft inside. He becomes quite conspicuous as he covers a classroom in snow, yells during an orientation speech and has other embarrassing moments. He soon learns that he is one of 113 students who are being prepared to confront the evil wizard Nettle and his huge Beast. Thornmallow feels he may not be equal to the challenge.
As you might guess by Henry's and the evil wizard's names, the naming convention follows plants, although the magic itself is based on singing (which is an issue for Thornmallow, as he's tone deaf).
“Said it now,” said Register Oakbend. “The Book says Better now than not But isn’t Henry a silly name? H-E-N-R-Y, don’t you know. Or H-E-N-R-I-E. Noth¬ ing to it. Simply a series of sounds without meaning. HEN-ER-REE. Now Couchwillow, there’s a good one. Or Stickybun. Or Daffy down-dilly, though that’s really for a girl. How about Broadleaf? Do you like it? Does it fit?”
....
“Magister Greybane,” he read silently. “Magister Bledwort. Magister Hyssop. Magister Briar Rose.” Something about the last wizard reminded Henry of his dear ma. Perhaps it was because she was the only one smiling. He said her name aloud: “Magister Briar Rose.”
Not matching is that he is living with his mother when she sends him away, and that most of the covers are pretty colorful, although the audiobook does have a very yellow cover.
I don't have a copy of the book in front of me, and it's not available for borrowing from the Internet Archive (only word searching), so I can't confirm if the way to the school requires instructions/words/counting, although there is apparently an enchanted road with a skipping rhyme talking about it. His mother does provision him for the road.
She was never one for delay. She stuffed the bag with a change of shirts, a pair of woollies for the cold, a packet of rose petals for the sweetening, and hard journeycake for the road.
....
Tell me the place where the wizards dwell,
Tell me each step and turning.
Over the mountains, under the hill,
Turn left and walk till morning.
