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will be a time lag between a name's first use in English and its
transphonation into Gaelic (assuming the name was not Gaelic to begin
with).

So names like Anne, Margaret, and Elizabeth start to get commingled not
too long after the Anglo-Norman invasion and settlement of Ireland, and
about the same time in Scotland as the Lowland and Highland cultures start
to interact more frequently.

Names that got borrowed into English later on take a longer time to filter
out to Scotland and Ireland (exception: French names catch on in Scotland
due to political and cultural connections).

One big caveat: in most cases the name will be spellied either all in
Gaelic or all in English, regardless of which culture it actually comes
from.

If you'd like more details I suggest you ask this question on the
AtlantianHeralds list or the Academy of S. Gabriel.

Evan