I'm brainstorming a character concept, a tavern brawler specialist that summons a variety of random items usually found in a bar (just because he is more familiar with those than regular weapons). He will be a level 3 Hexblade Warlock with Pact of Blade and have the Tavern Brawler feat.

I intend to utilize the third option of Tavern Brawler feat to grapple enemies hit by my pact weapon:

When you hit a creature with an unarmed strike or an improvised weapon on your turn, you can use a bonus action to attempt to grapple the target.

Tavern Brawler requires I hit with an improvised weapon, so I intend to summon, for instance, a kitchen knife, a bottle, or even a rolling pin or a pan, just for the hilariousity. And yes, the character will be a female dwarven innkeeper.

So, can I use Pact Weapon to summon improvised weapons? Or is the Pact Weapon required to be a conventional weapon? Can it be a kitchen knife that counts as dagger and improvised weapon?

No, you can't.

The Pact of the Blade pact boon states:

You can use your action to create a pact weapon in your empty hand. You can choose the form that this melee weapon takes each time you create it (see chapter 5 for weapon options).

On one hand, "Chapter 5" is the chapter about equipment, which - among other things - also describes the concept of improvised weapons (PHB, p. 147). Hence, they are a "weapon option [from chapter 5]".

Unfortunately, improvised weapons do not count as melee weapons (which the pact weapon is required to be), as explained in this question's answer.

Consequentially, you cannot summon improvised weapons as your pact weapon.

However ...

... the rules on improvised weapons also state the following:

In many cases, an improvised weapon is similar to an actual weapon and can be treated as such. For example, a table leg is akin to a club. At the DM's option,
a character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus.

Therefore, it would not deviate too much from RAW if your DM permitted you to e.g. summon a club reskinned as a table leg.

In any case, there shouldn't be any balancing issues whatsoever by allowing the summoning on improvised weapons as pact weapons.

Do note, however, that such a house rule might annoy other party members who have to take the tavern brawler feat to gain proficiency with improvised weapons. If you don't have a party member with this feat or if your DM requires you to take the feat as well to gain proficiency with summoned improvised weapons (contrary to the pact's description), then that shouldn't be a problem, though.