In Latin, -us marks the name as being (likely to be) masculine and the subject of a sentence. When Latin names are used in English, the second part is treated as irrelevant, but the association with gender is still apparent.
Like English, Latin makes use of suffixes to mark word inflection. Inflection means that the same word can take different forms depending on its function in a sentence: some examples of inflection in English are the difference between the singular noun dog and the plural noun dogs, or between the verb forms help, helps, and helped. But English has relatively few inflectional suffixes compared to Latin.
Latin nouns and adjectives change form depending on their function in a sentence. This is called 'case'. English has a remnant of this kind of distinction in pronouns, such as "I" vs. "me": "I" is used as a subject ("I run") whereas "me" is used as an object ("They saw me"). In Latin, ordinary nouns are also distinguished this way. "Titus currit" means "Titus runs" (with "Titus" as the subject of the verb), whereas "vident Titum" means "They see Titus" (with "Titum" as the direct object of the verb).
"Titus" is the form of the name that would be used as the subject of a verb. The name also has the forms "Titi", "Tito", "Titum", "Tite", each with their own use. But a common convention when mentioning Latin words in isolation is to cite the form used for the subject, so that is what got borrowed into English.
One last thing that should be mentioned is gender. Latin has three genders, or noun classes, called masculine, feminine, and neuter. As with modern Romance languages, many words for inanimate objects belong to the masculine or feminine noun class. However, words that denote male persons are almost always masculine, and words that denote female persons are almost always feminine: in this case, we can say that the noun class matches the word's 'natural gender'. In the case of personal names, in fact, I think the noun class always matches the natural gender.
The ending -us is specifically associated with the masculine gender*: the feminine counterpart of this ending is usually -a. Hence, the masculine name Julius has the feminine counterpart Julia, Flavius has Flavia, and many more names exist in masculine-feminine pairs like this. (In fact, at a certain time period in ancient Rome it was customary to refer to a woman by the feminine form of her father's family name; thus, Julia is the name of the daughter of Julius, Claudia is the name of the daughter of Claudius, etc. A name that ends in -ius or -ia is usually a family name, called in Latin a "nomen gentilicium".)
The -us in Jesus has a somewhat different etymology from the other names in your question. This name actually has irregular forms, but I won't elaborate as that doesn't change much about the overall concept.
*There are some exceptions to -us being a masculine ending: a small number of uncommon feminine nouns, and some neuter nouns (such as corpus, genus, tempus) that actually end in an unrelated but homophonous ending that is also spelled -us.