Figuring the SVO of the sentence "I'm Tom."

Not every sentence is SVO. SVO refers to the general pattern of those primary constituents for English and a variety of other languages when discussing language typology. It's not a language requirement.

Intransitive verbs in English, for example, don't need an object. In fact, they can't take an object:

• He died, for example, doesn't have an object.
• *He died poison, is not grammatical.

be (the copula) is a strange verb in most languages. Some would analyse simple sentences such as I am Tom as stative passive, with Tom being the complement of I.

Like Myqlarson said, SVO merely indicates a language typology, which basic elements order in a sentence is Subject-Verb-Object. This means that these elements are typically in this position, but in the middle you might put other elements (adjectives, adverbs); there might also exist exceptions in the same language to this rule.

In your case "I'm Tom", we need to treat it a little differently. That is because the verb "To be" is not a "predicative verb" or action verb (I'm not sure if the first is the right term), but a copular verb, also called linking verb.

The difference is that when you have a copular verb, the verb plays the role of defining the subject together with the element coming after it, such as in this case "I am Tom"; when you have an action verb, you're not defining the subject, but rather you're defining the action done by the subject (that "falls" on the object, in case there is one).

This last sentence is important because it touches your other question: not all verbs need an object, and not all verbs can stay there with only one object. This is called verb valency (I'll paste the scheme, the numbers indicate the objects taken):

1. an avalent verb takes no arguments, e.g. It rains. (Though it is technically the subject of the verb in English, it is only a dummy subject, that is a syntactic placeholder - it has no concrete referent. No other subject can replace it.);
2. a monovalent verb takes one argument, e.g. He¹ sleeps;
3. a divalent verb takes two, e.g. He¹ kicks the ball²;
4. a trivalent verb takes three, e.g. He¹ gives her² a flower³;
5. a tetravalent verb takes four. Sometimes bet is considered to be a tetravalent verb in English like in the example: The fool¹ bet him² five quid³ on "The Daily Arabian"⁴ to win.