Not all parts of a name are created equally. Many names include function words like articles and prepositions. For English speakers, this type of formation is somewhat unfamiliar; English names don't include the definite article the or the prepositions of. However, in other languages, surnames that include these words are very common.
Names that begin with function words create a number of difficulties for genealogists due to their often inconsistent treatment. There are three main issues you have to consider.
One or more words? There is a lot of variation in terms of whether the parts remain separate or are written as a single word. The preposition van "of" is characteristic of many Dutch names, including the 8th president of the United States, Martin Van Buren. It originally indicated the place of origin of the bearer of the surname and in Dutch it is left uncapitalized, Vincent van Gogh, literally Vincent of Gogh. In contrast, the Vanderbilt family, a prominent American family of Dutch origin, treats the name as a single word instead of van der Bilt "of de Bilt". You may also find in some cases a compromise where the name is written as a single word, but with internal capitalization, like VanBuren.
Disappearing words. The second issue is that from generation to generation or even record to record the function word may disappear and then reappear. For example, on the marriage record of my 6th great grandfather, Jean Baptiste Blais, his mother is listed as "marie marguerite roi":
However, on her own marriage record from June 13, 1726 in Saint-Vallier, Quebec, she is listed as "margueritte Le Roy":
Both records are available as a part of the Drouin Collection on ancestry.com.
Alphabetization. The final issue is how these words are alphabetized. You will find rules for alphabetization if you consult the MLA style guide or the Chicago Manual of Style, but don't expect these rules to be consistently followed. Be prepared to consider all options. This has been of special relevance to my research into my ancestors in Brittany.
In Lower Brittany names with a definite article are everywhere. My great grandmother, who was born in Nantes, had ancestry split between Lower and Upper Brittany. Her mother's ancestors were all from Lower Brittany, while her father's ancestors were from Upper Brittany. The division between the two parts of Brittany is partially linguistic. In Lower Brittany, Breton, a Celtic language, dominated, while, in Upper Brittany, Gallo and French, Romance languages, were the norm.
This linguistic divide is also reflected in the naming practices. I have 14 different surnames with the definite article Le among my ancestors in Lower Brittany, including Le Bourhis, Le Hiaric, Le Joudec and Le Bacquer. In contrast, I have yet to encounter such a name among my ancestors in Upper Brittany. In indexes from Lower Brittany, such as those from the commune of Plouguernével where many of my ancestors lived, names with an article are typically alphabetized by disregarding the article. For example, the name Le Bourhis is listed under "B" and is written as "Bourhis (le)". However, in indexes in Nantes where many in the family later migrated, the name Le Bourhis is found alphabetized by the letter "L" and is simply listed as "Le Bourhis". This does make some sense. In Plouguernével, because of how common names with the article are, it makes more sense to disregard it to avoid half the names being in the "L" section, but in Nantes where it is less common, this is less important.
In my own records, I generally take these names as a whole and just list the surname as "Le Bourhis". I think this is simpler and less confusing.