702.124f “Partner with [name]” is a variant of the partner ability. “Partner with [name]” represents two abilities. One is a static ability that modifies the rules for deck construction. Rather than a single legendary creature card, you may designate two legendary creature cards as your commander if each has a “partner with [name]” ability with the other’s name. You can’t designate two legendary cards as your commander if one has a “partner with [name]” ability and the other isn’t the named card. The other ability represented by “partner with [name]” is a triggered ability that means “When this permanent enters the battlefield, target player may search their library for a card named [name], reveal it, put it into their hand, then shuffle their library.”
You can choose Trynn and Silvar as your two commanders, starting both in your command zone. Color identities of white, black, and/or red would then be allowed among the other 98 cards.
If you have only one commander and it is mono-white (either Trynn or another mono-white commander), Silvar can not be among the other 99 cards. You can still use Trynn's ability to search and shuffle your library, but Silvar won't be there to be found.
With "partner with [name]" you may designate both Trynn and Silvar as your commander (C.R. 702.124f). If you do, your commander's color identity is white, black, and red, not just white, and you can include in your Commander deck—
Plains, Swamp, and Mountain cards, and
cards whose color identity is colorless or any combination of those colors (other than those with a basic land type)
(C.R. 702.124c, 903.4, 903.5c-d, 305.6).
Also, the triggered ability in "partner with [name]" works regardless of whether both Trynn and Silvar are your commander, or either of them, or neither of them (review C.R. 702.124f).
[c]Silvar, Devourer of the Free[/c] -> Silvar, Devourer of the Free
You can choose Trynn and Silvar as your two commanders, starting both in your command zone. Color identities of white, black, and/or red would then be allowed among the other 98 cards.
If you have only one commander and it is mono-white (either Trynn or another mono-white commander), Silvar can not be among the other 99 cards. You can still use Trynn's ability to search and shuffle your library, but Silvar won't be there to be found.
Also, the triggered ability in "partner with [name]" works regardless of whether both Trynn and Silvar are your commander, or either of them, or neither of them (review C.R. 702.124f).
EDIT (May 4, 2021): Add rule citation.