The name ‘Penda‘ is of unknown meaning.
First, it looks Welsh: ‘the good head’ : penn + da. The fact that it doesn’t really make much sense in Welsh and also that such a name does not exist in Welsh does not bring much confidence to this theory. But it cannot be denied that the name looks Welsh.
Here is an outlier explanation to the name.
First, there is marginal but plausible evidence for an Irish presence in the Welsh border region. Here we find such possibly Irish-related names such as Creoda and Crida and Cynric in both Mercia and Wessex. Cynric, for example, is phonetically more or less identical to the Irish name Cunorix, a name in fact attested in an inscription near Wroxeter: CVNORIX | MACVSM/A | QVICO[L]I[N]E.
(It should be noted too that there was substantial Irish settlement along the west coast of Wales, clustered especially around the Lleyn Peninsular and Dyfed.)
Now consider the Welsh name Cunedda (< Cunedag), name of the illustrious founder of the kingdom of Gwynedd and who in fact drove the Irish out of Lleyn. This British name is meaningless to an Irish speaker until it is corrupted into something like ‘Cenn-dag’. Of which the Welsh equivalent is ‘Penn-da’.
The idea is far-fetched and highly unlikely but 1) not impossible, 2) it does explain the name ‘Penda’.
It may be noted that Penda’s ill-fated son was named Peada, if anything even more obscure, but very similar in sound and form.
Penda’s father was Pybba, another possibly Welsh name, and his father was the Creoda mentioned above, which I think is from Irish ‘Cruth’ (‘Briton’). So the general background here does offer some support of a mixed British~Irish~English culture.