When Captain Picard was assimilated by the Borg, he lost his prior identity. He obviously was no longer on the side of the Federation, as he was actively working against it. And yet he still referred to Commander Riker as "Number One," as though that relationship continued, which, of course, wasn't true. Riker wasn't Locutus' Number One.

Is there an explanation for this?

Locutus is demonstrating to Riker that not only does he have Picard's tactical knowledge (of the Federation's defences) but that they also possess his personal memories.

The show script makes it abundantly clear that referring to Riker as "Number One" is their way of stressing the futility of resistance and attempting to unnerve Riker at the same time.

RIKER : (unbelievable) They couldn't have adapted that quickly...

LOCUTUS : (on the contrary) The knowledge and experience of the human Picard is part of... us now. It has prepared us for all possible
courses of action. Your resistance is hopeless (beat) Number One.

And on the frightening intimacy of the moment...on Riker's reaction...

In the subsequent episode, TNG : Family we learn that the Borg had complete access to his memories but also total control over his actions. His attempts to resist were utterly ineffectual:

PICARD : You don't know, Robert. You don't know. They took everything I was. They used me to kill and destroy. And I could
not stop them. I should have been able to stop them.

I tried... I tried... so hard...but I just wasn't strong enough. Not good enough. I should have been able to stop them. I should have been
able to...

That was the whole point.

The Borg specifically said that they assimilated Picard so that he could speak for them and facilitate Humanity's assimilation. In ST: First Contact they expanded upon this by revealing that the Queen wanted "a counterpart," but even in Locutus's first appearance his role is clearly more than that of a simple Borg Drone. He is supposed to be, in a twisted Borg sort of way, almost an ambassador, or perhaps a provincial administrator for a conquered territory. Picard later refers to Locutus as a "liason."

That means the Borg don't just want to take his raw knowledge, they also wanted him to serve as an intermediary or spokesman of sorts. Given that objective, it makes sense to refer to Riker in a way that Picard would naturally. Dropping the familiarity and personal knowledge that Picard held would have defeated the entire purpose of Picard's assimilation. They could hack a terminal if they just wanted everyone's names, and they'd already ordered the Enterprise to stand down and be assimilated through an impersonal audio communication. It didn't work, so they were changing tactics.

The Borg didn't want "Drone 89240931 of 95152645" to talk to "Commander William Thomas Riker of the United Federation of Planets."

They wanted Locutus to talk to his Number One.

There are a number of things this can be taken to imply, but I will point out two.

That Picard was resisting assimilation

One interpretation, and I believe the one that is intended, is that Picard was so strong willed that the attempts to suppress his identity were, at the very least, incomplete. This is later supported by Picard aiding in disabling the Borg later in the 2-parter.

That Picard had so engrained the identity of Riker as "Number One" in his mind, that the collective understands this as the commander's name

This makes the most logical sense to me. Picard was targeted for assimilation specifically for his knowledge of the Federation and humanity, to aid in the assimilation of the same. It is not that far of a stretch to believe that the Borg prioritized Picard's perception, of Riker in this case, over its own observations. This would include calling him "Number One"

The first poster is partly right, but the key point is that Picard, unbeknownst to the Borg, was communicating to Riker that he was still "there". Because of what the first poster said, the Borg did not catch on to this.

You guys are getting it wrong. The obvious reason was that Locutus wanted to disrespect Riker's status as captain now.
He knew Riker was in command of the ship, and Locutus made that remark as a swipe to him.
Riker wasn't scared when he said that. His expression was one of, "How dare you disrespect my status as captain!"
For someone who was rather an emotionaless borg, Locutus seems to remain human in a rather devilish way