According to the Wiktionary for the Old Norse name Ívarr:
The first part (Ív-) stems from Proto-Germanic *īwaz (“yew”), whence also Old English īw. The second part (-arr) stems from Proto-Germanic *harjaz (“warrior”), whence also Old Norse herr (“army, crowd”). Partly merged with Old Norse Yngvarr, Ingvarr.
About Álvaro, the same source presents the following etymology:
Álvaro and Álvara stem from the Late Latin proper name Alvarus, from Spanish-Visigothic. The Germanic proper name consists of two parts: The first part stems from *all- ("all") or from *adal- ("noble"). The second part stems from *-wars ("protection, defense"). However, there exist other etymologies.
Since the name Álvaro can also be found in Portuguese, one of these "other etymologies" is that Alvaro would have stemmed from Ælfred, related to Germanic alfi, "elf", radi, "counsel". The voicing (from [f] to [v]) could have been influenced by the Hispanic albar, derived from Latin albor (from albus, "white").
There is another, more far-fetched etymology: according to Meyer-Lübke, Romanische Namenstudien. I, 8, 81, II, 73, the name Álvaro stems from al-, "all", and *wars, "aware, circumspect"; another possibility for the second element is a derived form of the Gothic warjan. So, it would mean something like "he who is aware of everyone/everything" or "he who defends himself from everyone/everything".
It seems that the etymological evidence is quite weak and there is no consensus on the matter.