namentlich
by name
Means that something or someone is mentioned or listed by stating the specific name.
Die Gewinner des Wettbewerbs wurden alle namentlich auf der Bühne genannt.
The winners of the competition were all named on stage.

by name / especially
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by name
Means that something or someone is mentioned or listed by stating the specific name.
Die Gewinner des Wettbewerbs wurden alle namentlich auf der Bühne genannt.
The winners of the competition were all named on stage.

The adverb 'namentlich' (by name/especially) is derived directly from the noun 'der Name' (name). The ending '-lich' turns it into an adverb with the literal meaning 'by name'.
Die Verdächtigen sind der Polizei namentlich bekannt.
The suspects are known to the police by name.
'Namentlich' (by name/especially) is used mainly in written language and in formal contexts, for example in official documents, reports, or academic texts.
Alle Teilnehmer müssen sich namentlich registrieren lassen.
All participants must register by name.
In the meaning 'mit Namen' (by name), 'namentlich' often appears with verbs like 'nennen' (to name), 'erwähnen' (to mention), 'aufführen' (to list), or 'bekannt sein' (to be known).
Der Zeuge konnte den Täter nicht namentlich nennen.
The witness could not name the perpetrator.
You can often recognize the meaning 'insbesondere' (especially) from the sentence structure: First a general group is named, then 'namentlich' follows with one or more concrete examples from that group.
Einige europäische Städte, namentlich Paris und Rom, sind bei Touristen sehr beliebt.
Some European cities, especially Paris and Rome, are very popular with tourists.
especially / special
'besonders' and 'namentlich' can both single something out from a group. 'besonders' is the normal, broad word and fits in many situations when something is more important, stronger, or more special. 'namentlich' is much more specific and rather formal. It can mean that someone or something is named by name. It can also be used like 'insbesondere' (in particular / especially) when you single out a person or thing precisely. In everyday language, 'besonders' is usually more natural. 'namentlich' is more suitable in reports, lists, or official texts.

Im Bericht werden alle Helfer namentlich genannt.
All the helpers are named by name in the report.
Für die Prüfung ist besonders das letzte Kapitel wichtig.
For the exam, the last chapter is especially important.