Since you asked, here are the most of the possible parts of a name in English from my (BrE) perspective: You can skip to the bit about other languages if you wish; P.S> you seem to be asking about English and other languages(?)
First name (forename):
Pretty self-explanatory; the first part of someone's name. When you are informally addressing someone known, you will typically only use their first name.
Last (family) name:
Also straightforward, the last part of someone's name, in most cases taken from their father (their family name). You will typically introduce someone with their first and last name in a formal situation. The first and last names of a person are generally called their full name, though this sometimes includes their middle name(s)Lexico Oxford Dictionaries. In your case, the "Sánchez" part would be in English referred to as a maternal or matronymic surname. There's a lot more on this here.
These are the names that go in-between the first and last names, and are usually taken from grandparents/ancestors etc. A person can have several middle names.
John Edward Lawrence Smith
Nickname or moniker:
These informal titles are almost exclusively used in conversation between friends, and pretty much never formally. They are styled in writing usually like this:
John "Johnny" Smith
Honorary and Professional Titles:
You achieve these titles either through gaining a degree. First of all, a professional title is achieved through education (like a P.h.D [Doctorate] or MA[Master of Arts]). A knighthood or, in the UK, something like an Order of the British Empire (OBE) is achieved through services to your country. A hereditary title is inherited usually through parents e.g. "Count" or "Duke".
Note that if you are a doctor and are knighted, you would put the Sir at the beginning and the "Dr." would become "P.h.D" at the end:
Sir John Smith, P.h.D
In the same way, Count or some such takes precedence over Sir. There is more on this that is not of significant relevance here at Debrett's (via WayBackMachine)
There is loads more on complicated English naming customs than is appropriate here at Wikipedia.
In other languages,
Spanish, as in your case:
a person's name consists of a given name (simple or composite)
followed by two family names (surnames). Historically, the first
surname was the father's first surname, and the second the mother's
If you're very interested in the complications of the Spanish naming system, there's a very long and detailed description at Wikipedia, which listing here would be inappropriate: Spanish naming customs
To keep it simple and comprehendible:
All names taken from the mother are matronymic or maternal
All names taken from the father are patronymic or paternal
So, in an English description
Ana María is her personal forename (See my part about English above; this is how it links)
Gómez is her paternal surname(taking precedence over the maternal one
Sánchez is her maternal surname.
Hope this helps.