[name_u]River[/name_u], [name_m]Wilder[/name_m], and…
[name_m]Archer[/name_m]
[name_m]Booker[/name_m]
[name_u]Dylan[/name_u]
[name_u]Flynn[/name_u]
[name_m]Graham[/name_m]
[name_u]Hudson[/name_u]
[name_u]Jude[/name_u]
[name_u]Rhys[/name_u]
[name_m]Wyatt[/name_m]
[name_m]Zane[/name_m]
[name_u]Love[/name_u] [name_u]River[/name_u] & [name_m]Wilder[/name_m]! You’ve gotten some awesome suggestions and I want to say the first name (already suggested) that came to mind was Alder (a kind of tree). Though maybe [name_m]Wilder[/name_m] and Alder have too similar a sound?
Jarrah, it’s a type of Australian tree and a boy’s name here.
[name_u]Sky[/name_u]
[name_u]Rain[/name_u] (little boys I nannied were rain and north)
[name_u]Teal[/name_u] the male version of my name 
[name_u]Ash[/name_u]
You shoul definitely opt for a nature name. Having said that, I love your names [name_u]River[/name_u] and [name_m]Wilder[/name_m]!
You could use:
[name_u]Hunter[/name_u]
[name_m]Wolf[/name_m] (might be tad out there, so perhaps as a middle name?)
[name_m]Bjorn[/name_m]
[name_m]Archer[/name_m]
[name_u]Oakley[/name_u]
[name_u]River[/name_u], [name_m]Wilder[/name_m], and…
[name_u]Hunter[/name_u]
[name_m]Archer[/name_m]
[name_u]Everest[/name_u]
[name_m]Forrest[/name_m] (second favorite)
[name_u]Canyon[/name_u] (my favorite)
I [name_u]LOVE[/name_u] [name_u]Canyon[/name_u] and think it would go well with [name_u]River[/name_u] and [name_m]Wilder[/name_m] (nice change from the -er ending too).
[name_m]Gannon[/name_m]
[name_m]Bridger[/name_m]
[name_u]Finch[/name_u]
[name_u]Orion[/name_u]
[name_m]Greyson[/name_m]
[name_m]Irvine[/name_m]
[name_u]Roscoe[/name_u]
[name_m]Atlas[/name_m]
[name_m]Woodrow[/name_m]
[name_m]Ambrose[/name_m]
I really really really like your sons’ names, great choices!
[name_u]River[/name_u], [name_m]Wilder[/name_m] and…
[name_m]Fletcher[/name_m]
[name_m]Weston[/name_m]
[name_u]West[/name_u]
[name_m]Wolf[/name_m]
[name_m]Fox[/name_m]
[name_u]Hunter[/name_u]
[name_m]Hawk[/name_m]
[name_m]Forest[/name_m]
[name_m]Graham[/name_m]
[name_u]Bay[/name_u]
[name_u]Finch[/name_u]
[name_f]Sparrow[/name_f]
[name_m]Archer[/name_m]
[name_u]Sawyer[/name_u]
[name_m]Thatcher[/name_m]
[name_u]Harbor[/name_u]
[name_m]Cole[/name_m]
[name_m]Colt[/name_m]
[name_u]James[/name_u]
[name_m]Crow[/name_m]/Crowe
[name_m]Xander[/name_m]
[name_u]Walker[/name_u]
[name_m]Cooper[/name_m]
[name_m]Brooks[/name_m]
[name_u]Grey[/name_u]
[name_u]Red[/name_u]
If any of these were already posted, I second them. I think [name_m]Fletcher[/name_m], [name_u]Sawyer[/name_u], [name_u]Walker[/name_u], [name_m]Brooks[/name_m], [name_u]James[/name_u] (I don’t know why but to me it just fits), [name_u]Grey[/name_u] and [name_u]Red[/name_u] work best. I also like the suggestions of [name_u]Ash[/name_u] and [name_m]Hawthorne[/name_m]
[name_m]Archer[/name_m]
[name_m]Atlas[/name_m]
[name_m]Birch[/name_m]
[name_m]Cannon[/name_m]
[name_u]Canyon[/name_u]
[name_u]Finn[/name_u]
[name_m]Forest[/name_m]
[name_m]Hawk[/name_m]
[name_u]Hunter[/name_u]
[name_u]Lake[/name_u]
[name_m]Moss[/name_m]
[name_u]North[/name_u]
[name_u]Oak[/name_u]
[name_u]Orion[/name_u]
[name_u]Phoenix[/name_u]
[name_m]Ranger[/name_m]
[name_m]Rune[/name_m]
[name_u]Sage[/name_u]
[name_m]Slade[/name_m]
[name_u]Storm[/name_u]
[name_m]Talon[/name_m]
Tyme
[name_u]Walker[/name_u]
[name_m]Wheeler[/name_m]
[name_m]Wolf[/name_m]
[name_u]River[/name_u] and [name_m]Wilder[/name_m] are great names! I like the nature theme and I think that’s a good one to follow. [name_u]Phoenix[/name_u] is probably not the best fit when you already have a [name_u]River[/name_u], as anyone who hears it will think you are a fan of [name_u]River[/name_u] [name_u]Phoenix[/name_u] and [name_m]Wilder[/name_m] would be left out of the match, or saved, depending on how they feel about it but it is an imbalance. I don’t think it means it’s unusable, but I think many would avoid it for one/both of those reasons. (I would)
I don’t have any more suggestions to add but from the names suggested these are the ones I really like with [name_u]River[/name_u] and [name_m]Wilder[/name_m] and are of the more adventuresome naturalist than sporting type:
[name_u]Everest[/name_u]-This is actually the name that just popped in my head when I first read your post.
[name_m]Forest[/name_m]
[name_m]Mars[/name_m]
[name_m]Apollo[/name_m]
[name_m]Atlas[/name_m]
[name_u]Easton[/name_u]
[name_u]Rowan[/name_u]
[name_m]Caspian[/name_m]
[name_m]Leonel[/name_m]
[name_m]Caspian[/name_m]
[name_u]Egypt[/name_u]
[name_u]Indiana[/name_u]
[name_u]Phoenix[/name_u]
[name_m]Cassius[/name_m]
[name_m]Hart[/name_m]
I would avoid the er ending. Three names with the same ending is really matchy.
[name_u]Fable[/name_u]
[name_u]Finch[/name_u]
[name_u]Flynn[/name_u]
[name_m]Atticus[/name_m]
[name_m]Finnegan[/name_m]
[name_m]Abel[/name_m]
[name_u]River[/name_u] & [name_m]Wilder[/name_m] are beautiful names … Let’s see… I’m going to go with 2 syllable names that don’t start with R or W 
I’m probably not going to come up with something great for each letter but I will leave them here maybe someone else will…
[name_u]Aspen[/name_u]
Brishen
[name_m]Colten[/name_m]
[name_m]Dawson[/name_m]
[name_u]Ember[/name_u]
[name_m]Forest[/name_m]
[name_m]Grover[/name_m]
[name_m]Haywood[/name_m]
I
[name_f]Journey[/name_f]
Kota
[name_m]Lander[/name_m]
Mountain
N
[name_m]Orin[/name_m]
P
Q
S
T
U
Valient
[name_m]Xander[/name_m]
Yorrik
Z
… ?
[name_f]Hope[/name_f] you find the perfect name, congrats!
Mariner, [name_m]Cove[/name_m], [name_m]Dover[/name_m], Crest?