What is considered consciousness?

Consciousness is simply to know or awareness of contact.

Is it simply the ability to rationalize, analyze and most important concentrate? With or without ego?

What you describe there seems like thinking and pondering. Through thoughts ego arises and always associated with and unwholesome root. Also see: Tanhā Jālinī Sutta

Does consciousness dictate who we are?

Yes and no. Concies does not on its own does nothing to dictate who we are. We are formed due to past conditioning. This is decided by whether we react to the feelings arising from contact with craving, aversion and ignorance. E.g. you touch a soft fabric and think I want this. This creates fabrications and becoming.

The Sutta MN38: Mahatanhasankhaya Sutta might be helpful:

"Just as fire is classified simply by whatever requisite condition in dependence on which it burns — a fire that burns in dependence on wood is classified simply as a wood-fire, a fire that burns in dependence on wood-chips is classified simply as a wood-chip-fire; a fire that burns in dependence on grass is classified simply as a grass-fire; a fire that burns in dependence on cow-dung is classified simply as a cow-dung-fire; a fire that burns in dependence on chaff is classified simply as a chaff-fire; a fire that burns in dependence on rubbish is classified simply as a rubbish-fire — in the same way, consciousness is classified simply by the requisite condition in dependence on which it arises. Consciousness that arises in dependence on the eye & forms is classified simply as eye-consciousness. Consciousness that arises in dependence on the ear & sounds is classified simply as ear-consciousness. Consciousness that arises in dependence on the nose & aromas is classified simply as nose-consciousness. Consciousness that arises in dependence on the tongue & flavors is classified simply as tongue-consciousness. Consciousness that arises in dependence on the body & tactile sensations is classified simply as body-consciousness. Consciousness that arises in dependence on the intellect & ideas is classified simply as intellect-consciousness.

In Pali Buddhism, 'consciousness' ('vinnana') is the sense awareness or cognition that operates through the six sense organs to facilite: (i) seeing; (ii) hearing; (iii) smelling; (iv) tasting; (v) touching &; (iv) knowing of the mind's internal feelings, perceptions, moods, thoughts, images, etc.

To use a rough analogy, 'consciousness' can be compared to the mere reflecting of an image by a mirror. Consciousness only 'reflects' sense objects, like a mirror, that is all. Consciousness does not 'think' or 'analyse', just like a mirror does not think or analyse.

To quote:

And what is consciousness? These six are classes of consciousness: eye-consciousness, ear-consciousness, nose-consciousness, tongue-consciousness, body-consciousness, intellect-consciousness. This is called consciousness

SN 12.2

~~~

Dependent on eye & forms, eye-consciousness arises.

Dependent on ear & sounds, ear-consciousness arises...

Dependent on nose & aromas, nose-consciousness arises...

Dependent on tongue & flavors, tongue-consciousness arises...

Dependent on body & tactile sensations, body-consciousness arises...

Dependent on intellect (mano) & ideas, intellect-consciousness (mano-vinnana) arises.

The meeting of the three is sense contact.

MN 18

In Pali Buddhism, the ability to rationalize, analyse & concentrate are other functions of other kinds of mentality (called 'mano', 'nama', 'sankhara khandha', etc).

Each of these mental functions, be they consciousness ('vinnana'), intellect ('mano') or mental intention ('sankhara khandha'), can operate without ego or self ('atta'). 'Ego' or 'self' is a natural instinctual yet ignorant idea the mind imputes upon conscious experience & mental activity. (If interested, read more here).

In Buddhism, what 'we' are is a product of the mind's accumulated & conditioned intentions & thinking (sankhara khandha) & thus 'what we are' is essentially unrelated to consciousness itself (even though what 'we' are are thoughts about what the mind is conscious of).

In short, we are what we 'think' we are. What we think we are is called 'bhava' ('becoming' or 'existence') in Buddhism. To quote:

The craving that makes for further becoming (bhava) — accompanied by passion & delight, relishing now here & now there — i.e., craving for sensual pleasure, craving to be (bhava), craving not to be (vibhava): This, friend Visakha, is the origination of self-identification described by the Blessed One.

MN 44

The 'view' or 'belief' ('ditthi') of 'what we are' is what the mind clings or attaches to (rather than what the mind is conscious of). To quote again:

There are these five clingings to the aggregates, friend Visakha: clinging to the form (body) aggregate, clinging to the feeling (vedana) aggregate, clinging to the perception (sanna) aggregate, clinging to the fabricating aggregate (sankhara khandha), clinging to the consciousness (vinnana) aggregate. These five clingings to the aggregates are the self-identification ('sakkhaya ditthi') described by the Blessed One."

MN 44

For example, a small baby, before its mind/brain is mature enough to develop ideas of "me" & "I", is continually conscious of an image, sound, smell, taste & touch of a certain woman. Then one day, when the mind/brain became mature enough, it started to categorise (label & solidify) those images, sounds, smells, tastes & touches as "my mother". This categorising of "my mother" was the beginning of developing the ideas that dictate what we are or what we think ourselves to be.

To continue the original quote from above so to incorporate the process of thinking:

Dependent on eye & forms, eye-consciousness arises. The meeting of the three is contact. With contact as a requisite condition, there is feeling. What one feels, one perceives (labels in the mind). What one perceives, one thinks about. What one thinks about, one objectifies

MN 18

What "we" are, namely, "self-identification", is what the mind thinks & objectifies about.