Because there is a later day for patron deities themselves, I have to think of this as about patronage as an overall concept. Perhaps I'm wrong... here it is, regardless.
When I consider the word "patron", it has, for me, particular connotations. It's not simply a close relationship with a deity... The word directly relates to the form of relationship in Roman culture between a client, or supplicant, and patron. The client makes requests, the patron says "sure, and in return you can do this and this for me" and it is done. Like sponsorship. A bit different from, but definitely related to, a patron of particular artists and so on. So, your patron is someone you represent, someone you serve, someone your actions reflect upon. Someone who is willing to sponsor you in a sense, but to whom you owe in return. And because of where this word came from and its meaning, a patron goddess is still a patron, not a matron, which means something else. (Think a woman in charge of a dormitory.)
It is, indeed, a close bond, and it can happen a number of different ways. It may be a sort of contract that you enter into willingly. One god may pass you onto another - I've actually had this happen to me. On the other hand, you may have no choice in the matter whatsoever, and a god who has claimed you may not take "no" for an answer.
In different religions these relationships will take different forms. Some indeed have different terms for this sort of relationship, and might use the word "patron" sort of as a term more people are familiar with. In Heathenry, there are terms like "fulltrui", which indicates something like "best friend", "most true". It indicates a strong shared troth with this deity. It's more appropriate a term than "patron" because of the different forms Nordic relationships take from Roman ones.
You do not need a patron. I hate that current running under Neo-Paganism at the moment that everyone needs a patron, and that everyone will have one eventually, and even that you're somehow not a proper or "full" Pagan if you do not have one. Many people do not have a patron. A patron is not some sort of requirement, nor is it the sort of relationship every Pagan wishes to have - even Pagans very devoted to their gods. What's worse is that quite a few people have got this idea, either from others or from books, that every Eclectic Neo-Pagan needs two patrons - one male, one female - that they serve in ritual in sort of place of the Wiccan Lord and Lady. I cannot stress enough that this isn't so. Deities from other cultures and religions cannot be inserted into these roles. Being drawn to both a male and female deity is all very well but you have people, now, feeling that they need one of each and that they should worship them together in the same ritual. This can be, y'know, very bad. Particularly if these deities are from different cultures or don't like each other.
Do I need to recount the story of Loki and Selene? I should hope not. All I have to say is that the person in question is damn lucky he asked Selene to his circle and not, Fates forbid it, Athena or Artemis.
Anyway. Deeper relationships.
Deep relationships with my deities are very important for me, and the way I do things. Others may not feel that deepening a relationship is particularly important, so long as they honour them, and that's fine for those people. Me, I crave that deeper relationship. Not with everyone, of course. Some deities I do not honour actively at all, but acknowledge in hailing the gods generally or in passing. Some deities I honour on occasion, but am not close to, nor drawn to deepening those relationships. But I do share close bonds with some deities, and a desire to deepen those relationships further. I'll discuss those deities in detail in later entries.
So! to use myself as an example: Loki is my fulltrui, my close friend, my "patron", if you will. I am also close to Oðinn and wish to deepen that relationship further, but he is not my patron and I don't serve him in the way I would if that were so. (Thankfully - I don't think I'm cut out to be one of Oðinn's! He asks heavy things of his own.)
As an aside, the God and Goddess of my Hedgecraft - of Whom I have spoken earlier - are the only deities in that tradition/religion... as such, "patron" seems a weird and inappropriate word to apply to Them. I serve Them, and seek to know Them, and follow where They lead. Call that relationship what you will.