Is it possible to hide alignment of summoned monster?

I have a cleric pj who wants to hide his alignment: with spell 2 "Undetectable alignment" it is very easy.

But what about his summons?
May "Creatures on Table 10–1 marked with an “*” (of the same alignment than the summoner) take advantage of "Undetectable alignment" too?

If not, how could this cleric do to prevent a basic "detect" spell on his summons to reveal his true nature...?

Anyone seeing the creatures can make an appropriate knowledge check and know the alignment of a summoned creature. Basically anyone with the right education knows devils are lawful evil and this cannot be hidden.

I didn't speak of elementals or creatures with alignment like devils, demons, etc... it's not the problem.

The problem is my cleric don't want to show he is lawful or chaotic. If he summons animals, these animals will come with the same alignment.

a chaotic neutral CN cleric of Desna (deity CG) summons a eagle* lvl 1: the eagle will be celestial, but its alignment will be CN as the summoner.
So, a simple "detect chaos" will show this... And anyone will know the summoner is chaotic too.

For instance, the cleric want to hide he is "chaotic" and cleric from a chaotic deity.
He uses bluff and says that he is a cleric of Nethys (deity N). He uses the spell "Undetectable Alignment" to conceal the aura CG of his deity, but... if he summons a simple animal like the eagle*, the eagle will be always celestial (not a problem) and always CN.

But, if the cleric casts under "undetectable alignment", the animal like eagle:
1) will have their alignment concealed too, because that of the summoner is concealed by a spell?

2) not concealed, so if someone cast a simple detect chaos, the spell will reveal that the summoner (i.e the cleric CN) is "not chaotic" but its sumon is chaotic... the eagle* will betray its summoner...

anyone with the right education knows devils are lawful evil and this cannot be hidden.

But, if the cleric casts under "undetectable alignment", the animal like eagle:

1) will have their alignment concealed too, because that of the summoner is concealed by a spell?

2) not concealed

2. The summoned creatures will not "inherit" the caster's spell-effect.