Two things remain before the naming system covers everything you will meet in this course: what happens when the parent is a ring rather than a chain, and how to say where a double or triple bond sits. Neither introduces a new principle. Both are the existing rules applied to a slightly different skeleton.
Rings: the parent gets cyclo-
A ring parent is named by putting cyclo- in front of the root for the number of carbons in the ring. A six-membered saturated ring is cyclohexane, a five-membered one cyclopentane, a three-membered one cyclopropane. As a substituent hanging off something else, the same ring is cyclohexyl, cyclopentyl, cyclopropyl.
Numbering a ring is different in one respect only: a ring has no ends, so there is no "start at the left" to settle it. You choose the starting carbon and the direction yourself, subject to the same priorities as before — the principal characteristic group takes C1 if there is one, and otherwise you start at a substituted carbon and go round in whichever direction gives the lowest locants.
When there is only one substituent on the ring, no locant is written at all: it is methylcyclohexane, not 1-methylcyclohexane, because there is nowhere else the methyl could be. With two or more, the first-cited one is usually C1 and you number to keep the set low.
Ring or chain: which one is the parent?
When a ring and a chain are both present and neither contains a higher-priority functional group, the parent is the one with more carbons. A cyclohexane ring with a methyl on it is methylcyclohexane — the ring wins six to one. The same ring attached to an eight-carbon chain is a cyclohexyl-substituted octane, because the chain wins eight to six.
If a principal characteristic group is present, the rule above is overridden exactly as it was for chains: the parent must contain that group, whether the group is on the ring or on the chain.
Double and triple bonds
A double bond changes the suffix from -ane to -ene; a triple bond changes it to -yne. Each needs a locant, and the convention is that the locant is the lower-numbered of the two carbons the bond joins. A four-carbon chain with the double bond between C2 and C3 is but-2-ene; one with the double bond between C1 and C2 is but-1-ene.
Because a double bond occupies two carbons, the number you write is the first of the pair, and you never write both. Two double bonds take -diene with two locants: penta-1,3-diene.
When a multiple bond and a principal characteristic group are both present, the ranking from the previous section applies in full: the functional group takes the lower locant, and the multiple bond gets what is left. Both suffixes appear in the name, the multiple bond's first.
Take a six-carbon chain with an OH at one end and a double bond at the other. Numbered from the alcohol end, the OH is C1 and the double bond runs from C5: hex-5-en-1-ol. Numbered from the other end, the double bond starts at C1 and the OH is at C6: hex-1-en-6-ol. The alcohol outranks the double bond, so it claims the 1 and the first name is correct — even though the second gives the double bond the lower number.
When a molecule contains both a double and a triple bond and there is a genuine choice of direction, the double bond is given the lower locant.
A cyclohexene ring carries a methyl group, with the double bond between two ring carbons and the methyl on the carbon next to one of them.
Choose the parent. The ring, six carbons, containing the double bond: cyclohexene.
Number. A double bond in a ring is numbered so its two carbons are C1 and C2 — the bond takes the lowest possible locants before anything else is considered. That leaves two directions, and you pick the one giving the methyl the lower number.
Assemble. With the methyl on a carbon adjacent to the double bond, going the direction that reaches it sooner gives 3-methylcyclohex-1-ene, and the "1" is often dropped in practice as 3-methylcyclohexene.
Cis, trans, E and Z — a forward reference
A double bond fixes the two carbons it joins so they cannot rotate, which means a name like but-2-ene describes two genuinely different compounds: one with the two methyls on the same side of the double bond and one with them on opposite sides. The name so far cannot tell them apart.
The prefixes cis- and trans- do it informally when each alkene carbon carries one hydrogen and one other group — cis for same side, trans for opposite. The general system, which works no matter what the four groups are, is E and Z, and it uses the same priority rules that assign R and S to a stereocenter. That belongs with the Stereochemistry chapter and is developed there; for now it is enough to know that an alkene name is often incomplete without one of these prefixes, and that a question asking for "the full name" of an alkene is usually asking for it.
Benzene rings with two substituents
A benzene ring with two groups on it can have them in three relative positions, and these have their own names, used constantly and interchangeably with numbers:
Usually abbreviated to a single italic letter: o-xylene, m-xylene, p-xylene. This vocabulary becomes load-bearing in the Aromatic Chemistry chapter, where the entire question of directing effects is phrased in it — a substituent is called an ortho, para director or a meta director, and the words mean exactly what they mean here.
What carries forward
You can now name, or read the name of, essentially every compound in the remaining chapters. What is left is not more nomenclature but more chemistry, and from here the names are a tool rather than a topic. The two forward references in this section are real, though: E/Z is finished in Stereochemistry, and ortho/meta/para becomes the language of Aromatic Chemistry. Both will assume you met the words here.