To elaborate, I know it is illegal for authorities to question a suspect when their lawyer isn’t present. Is this a crime or just illegal? If it is a crime, what is it called?
"I know is it illegal for authorities to question a suspect when their lawyer isn’t present"
This is not really true, at least in the US. The suspect must explicitly ask for a lawyer. Even saying "Maybe I should talk to a lawyer" (ie Davis v. U.S. (512 U.S. 453 (1994)) isn't enough, they have to say "I want a lawyer". Until they invoke the right, an officer can question all they want (provided they were informed of these rights, except for certain situations which are relatively complicated. See Miranda Rights).
So no, an officer questioning you without a lawyer is neither a crime nor illegal. Once you invoke your Miranda right though, they have to respect that.
With or without your lawyer, this is called interrogation. You can filter your responses through a lawyer, or waive your right to a lawyer and answer directly.
In the United States, at least, there isn't a special term to capture this.
If the suspect has requested a lawyer, but the police continue questioning, you could call that a "Miranda violation," but tthat phrase could also refer to several other actions, such as failing to notify the suspect of his Miranda rights, or questioning him when he has not asked for a lawyer, but has invoked his right to remain silent.
In the United States, if someone who has requested a lawyer is questioned by police despite their desire not to do so, in violation of their Miranda rights under the 6th Amendment, this is a "civil rights violation".
There are several remedies for this civil rights violation.
It can trigger the exclusionary rule to exclude any statement obtained in that fashion from being used at trial against the person questioned. This happens routinely.
It can be a basis for a lawsuit against the interrogating officer for money damages for violating a well established constitutional right. This would be in the form of a 1983 action if the official is a state or local officer, and in the form of a common law Bivens action is the official is a federal official. This would be quite rare.
It could, in theory, also be the basis for a federal criminal prosecution of the interrogating officer for intentionally violating civil rights, although this would be almost unheard of unless the practice was pervasive.
A civil rights violation such as this would also provide a valid basis for disciplining or even firing the law enforcement officers for good cause. This also almost never happens.
I know it is illegal for authorities to question a suspect when their lawyer isn’t present.
This is not really true, at least in England and Wales.
The right to free and independent legal advice (FILA) is defined by s.58 of the Police and Criminal Evidence Act 1984 (PACE), but it is not an absolute right. It may be delayed - but not totally denied - under certain circumstances such as when a senior police officer reasonable believes that a consultation with a solicitor may, inadvertently or otherwise, lead to interfering with evidence, causing harm to others, tipping off other not yet arrested suspects, or hindering the recovery of property.
Similar criteria also apply when an "urgent interview" is necessary to secure time-critical evidence.
Any prosection evidence obtained unfairly by significant or substantial breaches of PACE may be excluded following a defence application under s.78 of PACE.
One example of when access to a solicitor was unfairly denied is the investigation in to the murder of Sian Callaghan. In essence, the officer concerned did not have an "urgent" need to conduct an interview.
If it is a crime, what is it called?
Unfair denial to FILA is called a "Breach of PACE" which is not a crime in-and-of-itself although there is the possibility of, for example, perverting the course of justice or misconduct in a public office offences.