What is the formal name for an "entry" in an ontology?
My understanding is that an ontology, at the end of the day, really boils down to some database storing objects/entries, where each entry has a set of known attributes as well as relationships to other entries.


The more common understanding is that one can emulate1 any ontology as a theory in single sorted first order predicate logic. Because such a theory can be seen as an ontology itself, it "really boils down to ... database(s)" if and only if predicate logic boils down to databases. And indeed, there is a close connection, but it won't help you to understand ontologies.


  What is the formal name for an “entry” in an ontology?


Even in your database analogy, you are missing the fact that you also have to specify the database scheme itself in the ontology language. There are different components of an ontology, namely individuals, types/classes, attributes, interrelationships/relations, function terms, restrictions, rules, axioms, and events1. Your "entry" seems to be intended to describe the attributes of an individual, and the relations between individuals. This task is done by the rules, but note that rules are more powerful than this.



1If the ontology contains events, then it is unclear how to emulate it in predicate logic.



Just like vzn, I now have the urge to clean up some of the confusion from the question, independent of whether it will earn me downvotes or not. (People might argue that such explanations based on mathematical logic require too much background knowledge, are too unrelated to ontology, and only lead to confusion. They may be right...) Even if there are practical reasons to prefer RDF or OWL as ontology languages over predicate logic, the simple structure of the later makes it a good tool for explaining some essential components of an ontology language.

A theory in single sorted first order predicate logic consists of axioms and a signature describing the non-logical symbols, i.e. the constants, functions, and predicates (and their arity). The axioms are well formed logical sentences over the given signature (with equality). Let's take set theory as an example. The signature just consists of $S_{rel}=\{\in\}$ and $\operatorname{ar}(\in)=2$, i.e. "$\in$" is a binary predicate. The axioms are logical sentences like $\forall A \, \forall B \, ( \forall X \, (X \in A \iff X \in B) \Rightarrow A = B)$ (Axiom of extensionality).

As an ontology, such a set theory has (at least) the following components:


a single type/class (sets),
a single interrelationship/relation (set $A$ is an element of set $B$ written as $A\in B$), 
and a set of axioms/rules


Further attributes and relations can be defined based on these, for example 


$\operatorname{singleton}(A) \iff \exists S \, (S \in A) \land \forall X \, \forall Y \, ((X \in A \land Y \in A)\ \Rightarrow\ X=Y)$
$A\subset B\ \iff\ \forall X \, (X \in A\ \Rightarrow X \in B)$


In single sorted first order predicate logic, you could use such attributes (as well as attributes that are part of the signature) to emulate further types/classes. One can also define constants (like the empty set $\{\}$) and functions (like union $\cup$) based on these. So individuals can be emulated as constants and function terms as functions.