There has not yet been an agreed consensus for a paediatric Long COVID case definition, but work is underway.

Long Covid is the patient-led term to describe the ongoing, fluctuating symptoms of COVID-19. Different organisations have decided to use slightly different names for the condition.

The WHO refers to Long Covid as Post COVID-19.  
On the 6th October 2021, the WHO issued the following definition;

  "Post COVID-19 condition occurs in individuals with a history of probable or confirmed SARS-CoV-2 infection, usually 3 months from the onset of COVID-19 with symptoms that last for at least 2 months and cannot be explained by an alternative diagnosis. Common symptoms include fatigue, shortness of breath, cognitive dysfunction but also others (see Table 3 and Annex 2) which generally have an impact on everyday functioning. Symptoms may be new-onset, following initial recovery from an acute COVID19 episode, or persist from the initial illness. Symptoms may also fluctuate or relapse over time. A separate definition may be applicable for children"

In the UK, The National Institute for Health and Clinical Excellence (NICE), the Scottish Intercollegiate Guidelines Network (SIGN), and the Royal College of General Practitioners (RCGP) include two conditions within the umbrella of Long Covid.

Ongoing symptomatic COVID-19
Persistent signs and symptoms of COVID-19 from 4 to 12 weeks
Post-COVID-19 syndrome
Persistent signs and symptoms that develop during or after an infection consistent with COVID-19, continue for more than 12 weeks and are not explained by an alternative diagnosis.

See their booklet here.

In the USA Long Covid is called PACS Post Acute Covid Syndrome. 
In the UK NICE released its 'living' guidelines using the name Post Covid Syndrome, this name is rarely ever used by people living with Long Coivd because it makes no sense to the people living with Long Covid. However, the 3 stages defined by NICE are often referred to by doctors. In the UK any adult or child with ongoing symptoms of more than 4 weeks is eligible for a referral to a Long Covid clinic/hub if the local paediatric team are unable to support locally.