AsThe first retail store keeper in Monterey was probably Don David Spence, born 24 October 1798 in the parish of Huntly, Scotland to David Spence and his wife Helen Stewart:
(registration required to access this birth record. Due to copyright restrictions I am unable to post the image)
Scotlands People
He died 18 February 1875 in Monterey and there is a memorial to him in the Monterey City Cemetery:
https://www.findagrave.com/memorial/42878080/don-david-spence
There is a short page on the Monterey County Historical Society which has a brief summary of his life including the fact that he opened a shop in Monterey:
http://mchsmuseum.com/spence_david.html
The justification for this answer is as follows:
In November 1826 Captain F W Beechey of HMS Blossom, then anchored in San Francisco Bay, dispatched three of his officers overland to Monterey in search of supplies. In his "Narrative of a voyage to the Pacific and Beering's strait" he describes their arrival at Monterey:
https://archive.org/details/narrativeofvoyag02beec/page/56/mode/2up
(my literal transcription of the published book, hence ownward, not onward)
As they approached the town, pasture lands, covered with herds of
cattle succeeded this wild scenery: and riding ownward, trees of
luxuriant growth, houses scattered over the plain, the fort, and the
shipping in the bay, announced the speedy termination of their
journey. At five o'clock in the evening they alighted in the square at
Monterey, and met a kind reception from Mr Hartnell, a merchant
belonging to the firm of Begg and Co. in Lima, who was residing there,
and who pressed them to accept the use of his house while they
remained in the town-an offer of which they thankfully availed
themselves.............
......Upon enquiry after the stores and medicines the ship stood in
need of, the result was highly unfavourable; as there were no
medicines to be had, and some stores which were essential to the ship
could nowhere be procured. The exchange on bills was favourable, but
there was no specie: Mr. Marsh therefore purchased what stores he
could from the inhabitants and from the shipping in the
roads..........
In January 1827 the Blossom arrived at Monterey to collect the stores that had been purchased:
We dropped our anchor in Monterey Bay on the first of January, and
with the permission of the governor, D.Miguel Gonzales, immediately
commenced cutting the spars we required; for each of which we paid a
small sum. Through the assistance of Mr. Hartnell, we procured several
things from the missions which we should otherwise have sailed
without, and our thanks are further due to him for his kindness and
attention during our stay.
It seems fairly clear from this that in January 1827 there was no retail store in Monterey, though the firm of McCulloch Hartnell and Company had been granted permission to build one in 1823, according to the following extract from the "The Lives of William Hartnell" by Susanna Bryant Dakin:
After the customary exchange of compliments, the Englishman[Hartnell]
explained to His Excellency[the Governor] that the maintenance of a
commercial house in the country necessitated freedom of more ports as
well as permission to build warehouses in scattered sites along the
coast. Here produce could be kept, and he needed at least one store in
which to sell at retail. He also protested against excessively high
duties on imports. Don Luis listened sympathetically to Don
Guillermo’s[Guillermo Arnel=Hartnell] complaints. Without forcing him
to endure the long wait for permission to come from Mexico City, the
Governor granted to Macala[=McCulloch] y Arnel the right “to trade in
all the ports of California and also in all the landfalls and bays
nearest the missions.” This was a real triumph over competitors who
were obliged to anchor either in San Diego or Monterey. Arguello
seemed reasonable about duties, and on May 21, 1823, had acceded to
the partners’ request that they be granted land and permitted to build
any needed warehouses, stores, or residences in the ports of Monterey
and San Pedro. So the new firm became solidly established.
Dakin also says, as Aaron has mentioned in his answer:
Early in 1823, the British firm had obtained a spacious adobe to be
used as a ‘tienda.’
However there is no further mention in Dakin to suggest that a physical retail store or shop was set up nor is there any mention of such an establishment in any of the 150+ documents, mainly letters, that I have examined.
Adele Ogden, in her article "Hides and Tallow: McCulloch, Hartnell and Company 1822-1828" in the California Historical Society Quarterly of September 1927 says:
https://nuhis220a.files.wordpress.com/2018/10/hides-tallow-article-by-ogden-1927.pdf
What were the general trading methods of McCulloch, Hartnell and
Company? As soon as a company ship had dropped anchor in Monterey Bay,
the captain delivered to Hartnell business letters from the main firm
in South America and the invoice of the ship's cargo. Shortly
thereafter, circular letters, announcing the arrival of the brig and
enclosing a list of goods aboard, were dispatched to the northern and
southern mission fathers. Within a week or so, the recently arrived
vessel proceeded southward, touching at specified collection depots.
At each port samples of the ship's cargo were exhibited, goods
delivered to the missions, future order lists made out by the friars,
and hides and tallow taken aboard. From San Diego, where stowage was
completed, the ship sailed for South America or England.
Again there is no mention of any retail store.
There is evidence though that William Hartnell was retailing, perhaps on his own account as opposed to on the partnership account, judging from this statement of John Milligan's account with William Hartnell for the period from November 30th 1822 to 10th January 1829:
https://archive.org/details/documentos2455129997vall/page/n184/mode/2up
Referring again to Dakin, Hartnell had an assistant/employee called David Spence:
The wedding of William Edward Petty Hartnell and Maria Teresa de la
Guerra was planned to take place in Santa Barbara on the last day of
April 1825, when the bride would be sixteen and the groom just turned
twenty-seven. Don Guillermo had little time for singing and dancing
with his future relatives in the spring days that preceded his
wedding. In the first place, there was the necessity of preparing a
proper home in Monterey for his bride of distinguished family and
luxurious upbringing. He now had the aid, in this personal project as
well as in company business, of a good-natured Scotsman named David
Spence, sent up from Lima in September. McCulloch had introduced him
as “my friend Mr. Spence, who you will find of the greatest service to
you.”
And Dakin states that David Spence operated a general store in Monterey after his contract with Hartnell expired. It may be assumed that this was in late 1828 or 1829:
After Hartnell’s return from South America[in July 1828,he'd journeyed
there to discuss the dissolution of the partnership] his business
decreased in volume and he, by necessity, managed it alone. His former
associates, McCulloch, Logan, and Fraser, no longer were in the
country; and David Spence went into business for himself when his
contract time expired. He stayed on in Monterey, operating a general
store and engaging in various trading ventures.
So in summary it would seem that whilst McCulloch Hartnell and Company, or at least William Hartnell on his own account, were the first retailers in Monterey, David Spence was probably the first retail store or shop keeper.
May I also, as a distant cousin of (Hugh) McCulloch mentioned in Aaron's answer may I just correct the impression that he "split". He was writing letters with instructions to Hartnell from different missions in California until at least 14 August 1823 and on 1 March 1824 he writes from Mazatlan which he was temporarily visiting being by then based in Callao:
After the business of McCulloch & Hartnell and Company was wound up Hartnell failed to pay his share of the losses and on 2 June 1831 McCulloch wrote to Hartnell:
I realise this last part of the answer does not relate directly to the question but I do wish to make it clear that from all accounts and by this and other actions Hugh McCulloch(1793-1842) was an honourable man.