Nomen possessoris in albo facile inventu est.

The sentence breaks down like this:

• nomen = the subject, name
• possessoris = a genitive depending on nomen, so of the owner / possessor
• in albo = a prepositional phrase, on the board / list
• facile inventu est = the predicate, is easy to find

So the core structure is:

The owner’s name + on the board + is easy to find.

Latin does not have articles like English the and a/an. Whether something is definite or indefinite usually has to be understood from context.

So nomen possessoris can, depending on context, be translated as:

• the owner’s name
• an owner’s name
• owner’s name

In normal English, this sentence will usually come out as the owner’s name.

Possessoris is the genitive singular of possessor. The genitive often shows possession or close association.

So:

• nomen possessoris = the name of the owner
• more naturally in English, the owner’s name

This is a very common Latin pattern. For example:

• liber pueri = the boy’s book
• vox magistri = the teacher’s voice

The preposition in takes the ablative when it means location, that is, in or on somewhere.

So:

• in albo = on the board / in the list / on the notice-board

Here albo is the ablative singular.

If Latin wanted to express motion into or onto something, it would normally use the accusative instead. So the ablative here tells you this is about where the name is located, not where it is being moved.

Yes, it is related.

In Latin, album originally meant something white, especially a whitened board or tablet. Such boards were used for public notices or official lists, so album came to mean a notice-board, register, or list.

English album ultimately comes from this same Latin word, though its meaning shifted over time.

Here it is best understood as an adjective: easy.

It is the neuter singular form, matching nomen, which is also neuter singular. So the sense is:

• nomen ... facile est = the name is easy

Then inventu completes the idea: easy to find.

This can confuse learners because facile can also be an adverb in other contexts. But in this sentence, with nomen as a neuter singular subject, the adjectival interpretation makes the best sense.

Inventu is the supine in -u of invenio.

This is a relatively uncommon verbal form in Latin, and English does not really have a direct equivalent. In this construction it means something like:

• to find
• in finding
• with respect to finding

So facile inventu est means is easy to find.

A famous similar type is:

• mirabile dictu = wonderful to say
• horribile dictu = horrible to say

Because this is a standard Latin idiom: adjective + supine in -u.

The supine in -u is often used with adjectives to describe something in respect to an action. So:

• facile inventu = easy to find
• difficile factu = hard to do
• mirabile visu = wonderful to see

English usually translates this with to + verb, but Latin often prefers the supine in this kind of expression.

The main finite verb is est, meaning is.

Everything else is built around it:

• nomen possessoris = the subject phrase
• in albo = where the name is
• facile inventu = what is being said about the name

So the full statement is that the owner’s name is easy to find on the board.

Latin word order is fairly flexible because the endings show the grammatical relationships. So the meaning would still be clear in other orders, such as:

• In albo nomen possessoris facile inventu est.

However, not all word orders are equally natural. In the given sentence, nomen possessoris stays together nicely as a unit, and est comes at the end, which is very normal Latin style.

So yes, the order can change, but the original order is clear and idiomatic.