It has to be said, I am not a lawyer and this is not "legal advice".
Trademark registration does not actually give you 'trademark protection', trademark protection is established the moment you use the mark in commerce. So, if your name is original and qualifies as protected (see below), you would simply need to use it on your products and website and you'll have your very own protected 'Trademark', no registration required. It may be important to keep records of you using your mark in commerce as of a particular date, (think, photo of you and your labeled product at a farmers market) so you have standing if someone comes along in the future and tries to bully you off of it.
A word on trademark-ability... Words that are descriptive of the goods or services sold as well as surnames (unless the word also has a common use) cannot typically be registered or protected by trademark. For example, Sanchez Farms is likely not 'protected' as Sanchez is predominantly used as a surname and 'Farms' is descriptive of the product/service. There are many caveats to this and it boils down to your particular scenario, but you can likely use your surname for a farm without issue, unless it's ultra prevalent and confusing. For example, if your surname is 'Pepperidge' and you sell wholesome baked goods, I would avoid trying to use 'Pepperidge Farm' in any sort of commerce. The down side to this is that someone could potentially also use the same unprotected name and benefit from your good standing in the marketplace.
Business formation and LLC's in particular. Please take time to consider the benefits and protection of forming a business entity for your goods/services. This is an extremely personal choice, but in most states starting a business (legally creating a business entity, an LLC in particular) is quick, painless and far less costly than you might expect. For example, in my state, you can file online, through the Secretary of State's website, for a fee of $160 and become a legal entity instantly. There are several reasons to do this, but the most important in my opinion, is the protection you gain as it separates your personal assets (and liability) from your business's assets. LLC's in particular are designed to do this quickly and efficiently, and mean that (unless there is gross or criminal negligence) you are only liable, if sued, up to the assets your business owns, not you personally. In a farm setting, consider this... you form an LLC and 'lease' your private farm land to the LLC. If someone (Heaven forbid) gets sick or dies from the use or consumption of your product, they typically can only come after assets the LLC actually owns, which in this case, would not be your house/land. It's not a license to be sloppy, but if this same scenario happened without LLC separation and protection, you would have unlimited personal liability and could potentially lose everything.
Best wishes with naming your farm and selling your goods.