The Spanish Argimiro comes from the Medieval
Argimirus, Latinisation of a Germanic personal name (of Visigothic tradition). The first element,
argi, is from doubtful etymology:
a) maybe related with the old
German *arga, "shy, prudent, cautious" and also "miser" (De
Felice);
b) from the Germanic
aircan/ercan, "free, sincere, authentic, noble" (Tibón);
c) from
*harjis, variant of
hari, "army" (J.M. Piel).
The second element is, as you pointed, the Germanic element
mir, a variant of
mar, "famous".
Lumia
http://onomastica.mailcatala.com